3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
273 =head3 Changes since isl-0.19
277 =item * Zero-dimensional objects of type C<isl_multi_pw_aff> or
278 C<isl_multi_union_pw_aff> can now keep track of an explicit domain.
279 This explicit domain, if present, is taken into account
280 by various operations that take such objects as input.
286 C<isl> is released under the MIT license.
290 Permission is hereby granted, free of charge, to any person obtaining a copy of
291 this software and associated documentation files (the "Software"), to deal in
292 the Software without restriction, including without limitation the rights to
293 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
294 of the Software, and to permit persons to whom the Software is furnished to do
295 so, subject to the following conditions:
297 The above copyright notice and this permission notice shall be included in all
298 copies or substantial portions of the Software.
300 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
301 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
302 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
303 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
304 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
305 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
310 Note that by default C<isl> requires C<GMP>, which is released
311 under the GNU Lesser General Public License (LGPL). This means
312 that code linked against C<isl> is also linked against LGPL code.
314 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
315 will link against C<imath>, a library for exact integer arithmetic released
316 under the MIT license.
320 The source of C<isl> can be obtained either as a tarball
321 or from the git repository. Both are available from
322 L<http://isl.gforge.inria.fr/>.
323 The installation process depends on how you obtained
326 =head2 Installation from the git repository
330 =item 1 Clone or update the repository
332 The first time the source is obtained, you need to clone
335 git clone git://repo.or.cz/isl.git
337 To obtain updates, you need to pull in the latest changes
341 =item 2 Optionally get C<imath> submodule
343 To build C<isl> with C<imath>, you need to obtain the C<imath>
344 submodule by running in the git source tree of C<isl>
349 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
351 =item 2 Generate C<configure>
357 After performing the above steps, continue
358 with the L<Common installation instructions>.
360 =head2 Common installation instructions
364 =item 1 Obtain C<GMP>
366 By default, building C<isl> requires C<GMP>, including its headers files.
367 Your distribution may not provide these header files by default
368 and you may need to install a package called C<gmp-devel> or something
369 similar. Alternatively, C<GMP> can be built from
370 source, available from L<http://gmplib.org/>.
371 C<GMP> is not needed if you build C<isl> with C<imath>.
375 C<isl> uses the standard C<autoconf> C<configure> script.
380 optionally followed by some configure options.
381 A complete list of options can be obtained by running
385 Below we discuss some of the more common options.
391 Installation prefix for C<isl>
393 =item C<--with-int=[gmp|imath|imath-32]>
395 Select the integer library to be used by C<isl>, the default is C<gmp>.
396 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
397 for values out of the 32 bit range. In most applications, C<isl> will run
398 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
401 =item C<--with-gmp-prefix>
403 Installation prefix for C<GMP> (architecture-independent files).
405 =item C<--with-gmp-exec-prefix>
407 Installation prefix for C<GMP> (architecture-dependent files).
415 =item 4 Install (optional)
421 =head1 Integer Set Library
423 =head2 Memory Management
425 Since a high-level operation on isl objects usually involves
426 several substeps and since the user is usually not interested in
427 the intermediate results, most functions that return a new object
428 will also release all the objects passed as arguments.
429 If the user still wants to use one or more of these arguments
430 after the function call, she should pass along a copy of the
431 object rather than the object itself.
432 The user is then responsible for making sure that the original
433 object gets used somewhere else or is explicitly freed.
435 The arguments and return values of all documented functions are
436 annotated to make clear which arguments are released and which
437 arguments are preserved. In particular, the following annotations
444 C<__isl_give> means that a new object is returned.
445 The user should make sure that the returned pointer is
446 used exactly once as a value for an C<__isl_take> argument.
447 In between, it can be used as a value for as many
448 C<__isl_keep> arguments as the user likes.
449 There is one exception, and that is the case where the
450 pointer returned is C<NULL>. Is this case, the user
451 is free to use it as an C<__isl_take> argument or not.
452 When applied to a C<char *>, the returned pointer needs to be
457 C<__isl_null> means that a C<NULL> value is returned.
461 C<__isl_take> means that the object the argument points to
462 is taken over by the function and may no longer be used
463 by the user as an argument to any other function.
464 The pointer value must be one returned by a function
465 returning an C<__isl_give> pointer.
466 If the user passes in a C<NULL> value, then this will
467 be treated as an error in the sense that the function will
468 not perform its usual operation. However, it will still
469 make sure that all the other C<__isl_take> arguments
474 C<__isl_keep> means that the function will only use the object
475 temporarily. After the function has finished, the user
476 can still use it as an argument to other functions.
477 A C<NULL> value will be treated in the same way as
478 a C<NULL> value for an C<__isl_take> argument.
479 This annotation may also be used on return values of
480 type C<const char *>, in which case the returned pointer should
481 not be freed by the user and is only valid until the object
482 from which it was derived is updated or freed.
486 =head2 Initialization
488 All manipulations of integer sets and relations occur within
489 the context of an C<isl_ctx>.
490 A given C<isl_ctx> can only be used within a single thread.
491 All arguments of a function are required to have been allocated
492 within the same context.
493 There are currently no functions available for moving an object
494 from one C<isl_ctx> to another C<isl_ctx>. This means that
495 there is currently no way of safely moving an object from one
496 thread to another, unless the whole C<isl_ctx> is moved.
498 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
499 freed using C<isl_ctx_free>.
500 All objects allocated within an C<isl_ctx> should be freed
501 before the C<isl_ctx> itself is freed.
503 isl_ctx *isl_ctx_alloc();
504 void isl_ctx_free(isl_ctx *ctx);
506 The user can impose a bound on the number of low-level I<operations>
507 that can be performed by an C<isl_ctx>. This bound can be set and
508 retrieved using the following functions. A bound of zero means that
509 no bound is imposed. The number of operations performed can be
510 reset using C<isl_ctx_reset_operations>. Note that the number
511 of low-level operations needed to perform a high-level computation
512 may differ significantly across different versions
513 of C<isl>, but it should be the same across different platforms
514 for the same version of C<isl>.
516 Warning: This feature is experimental. C<isl> has good support to abort and
517 bail out during the computation, but this feature may exercise error code paths
518 that are normally not used that much. Consequently, it is not unlikely that
519 hidden bugs will be exposed.
521 void isl_ctx_set_max_operations(isl_ctx *ctx,
522 unsigned long max_operations);
523 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
524 void isl_ctx_reset_operations(isl_ctx *ctx);
526 In order to be able to create an object in the same context
527 as another object, most object types (described later in
528 this document) provide a function to obtain the context
529 in which the object was created.
532 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
533 isl_ctx *isl_multi_val_get_ctx(
534 __isl_keep isl_multi_val *mv);
537 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
539 #include <isl/local_space.h>
540 isl_ctx *isl_local_space_get_ctx(
541 __isl_keep isl_local_space *ls);
544 isl_ctx *isl_set_list_get_ctx(
545 __isl_keep isl_set_list *list);
548 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
549 isl_ctx *isl_multi_aff_get_ctx(
550 __isl_keep isl_multi_aff *maff);
551 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
552 isl_ctx *isl_pw_multi_aff_get_ctx(
553 __isl_keep isl_pw_multi_aff *pma);
554 isl_ctx *isl_multi_pw_aff_get_ctx(
555 __isl_keep isl_multi_pw_aff *mpa);
556 isl_ctx *isl_union_pw_aff_get_ctx(
557 __isl_keep isl_union_pw_aff *upa);
558 isl_ctx *isl_union_pw_multi_aff_get_ctx(
559 __isl_keep isl_union_pw_multi_aff *upma);
560 isl_ctx *isl_multi_union_pw_aff_get_ctx(
561 __isl_keep isl_multi_union_pw_aff *mupa);
563 #include <isl/id_to_ast_expr.h>
564 isl_ctx *isl_id_to_ast_expr_get_ctx(
565 __isl_keep isl_id_to_ast_expr *id2expr);
567 #include <isl/point.h>
568 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
571 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
574 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
576 #include <isl/vertices.h>
577 isl_ctx *isl_vertices_get_ctx(
578 __isl_keep isl_vertices *vertices);
579 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
580 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
582 #include <isl/flow.h>
583 isl_ctx *isl_restriction_get_ctx(
584 __isl_keep isl_restriction *restr);
585 isl_ctx *isl_union_access_info_get_ctx(
586 __isl_keep isl_union_access_info *access);
587 isl_ctx *isl_union_flow_get_ctx(
588 __isl_keep isl_union_flow *flow);
590 #include <isl/schedule.h>
591 isl_ctx *isl_schedule_get_ctx(
592 __isl_keep isl_schedule *sched);
593 isl_ctx *isl_schedule_constraints_get_ctx(
594 __isl_keep isl_schedule_constraints *sc);
596 #include <isl/schedule_node.h>
597 isl_ctx *isl_schedule_node_get_ctx(
598 __isl_keep isl_schedule_node *node);
600 #include <isl/ast_build.h>
601 isl_ctx *isl_ast_build_get_ctx(
602 __isl_keep isl_ast_build *build);
605 isl_ctx *isl_ast_expr_get_ctx(
606 __isl_keep isl_ast_expr *expr);
607 isl_ctx *isl_ast_node_get_ctx(
608 __isl_keep isl_ast_node *node);
610 #include <isl/stride_info.h>
611 isl_ctx *isl_stride_info_get_ctx(
612 __isl_keep isl_stride_info *si);
614 #include <isl/fixed_box.h>
615 isl_ctx *isl_fixed_box_get_ctx(
616 __isl_keep isl_fixed_box *box);
620 C<isl> uses two special return types for functions that either return
621 a boolean or that in principle do not return anything.
622 In particular, the C<isl_bool> type has three possible values:
623 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
624 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
625 C<isl_bool_error> (a negative integer value), indicating that something
626 went wrong. The following function can be used to negate an C<isl_bool>,
627 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
630 isl_bool isl_bool_not(isl_bool b);
632 The C<isl_stat> type has two possible values:
633 C<isl_stat_ok> (the integer value zero), indicating a successful
635 C<isl_stat_error> (a negative integer value), indicating that something
637 See L</"Error Handling"> for more information on
638 C<isl_bool_error> and C<isl_stat_error>.
642 An C<isl_val> represents an integer value, a rational value
643 or one of three special values, infinity, negative infinity and NaN.
644 Some predefined values can be created using the following functions.
647 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
648 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
649 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
650 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
651 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
652 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
654 Specific integer values can be created using the following functions.
657 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
659 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
661 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
662 size_t n, size_t size, const void *chunks);
664 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
665 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
666 The least significant digit is assumed to be stored first.
668 Value objects can be copied and freed using the following functions.
671 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
672 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
674 They can be inspected using the following functions.
677 long isl_val_get_num_si(__isl_keep isl_val *v);
678 long isl_val_get_den_si(__isl_keep isl_val *v);
679 __isl_give isl_val *isl_val_get_den_val(
680 __isl_keep isl_val *v);
681 double isl_val_get_d(__isl_keep isl_val *v);
682 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
684 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
685 size_t size, void *chunks);
687 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
688 of C<size> bytes needed to store the absolute value of the
690 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
691 which is assumed to have been preallocated by the caller.
692 The least significant digit is stored first.
693 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
694 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
695 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
697 An C<isl_val> can be modified using the following function.
700 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
703 The following unary properties are defined on C<isl_val>s.
706 int isl_val_sgn(__isl_keep isl_val *v);
707 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
708 isl_bool isl_val_is_one(__isl_keep isl_val *v);
709 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
710 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
711 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
712 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
713 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
714 isl_bool isl_val_is_int(__isl_keep isl_val *v);
715 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
716 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
717 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
718 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
720 Note that the sign of NaN is undefined.
722 The following binary properties are defined on pairs of C<isl_val>s.
725 isl_bool isl_val_lt(__isl_keep isl_val *v1,
726 __isl_keep isl_val *v2);
727 isl_bool isl_val_le(__isl_keep isl_val *v1,
728 __isl_keep isl_val *v2);
729 isl_bool isl_val_gt(__isl_keep isl_val *v1,
730 __isl_keep isl_val *v2);
731 isl_bool isl_val_ge(__isl_keep isl_val *v1,
732 __isl_keep isl_val *v2);
733 isl_bool isl_val_eq(__isl_keep isl_val *v1,
734 __isl_keep isl_val *v2);
735 isl_bool isl_val_ne(__isl_keep isl_val *v1,
736 __isl_keep isl_val *v2);
737 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
738 __isl_keep isl_val *v2);
740 Comparisons to NaN always return false.
741 That is, a NaN is not considered to hold any relative position
742 with respect to any value. In particular, a NaN
743 is neither considered to be equal to nor to be different from
744 any value (including another NaN).
745 The function C<isl_val_abs_eq> checks whether its two arguments
746 are equal in absolute value.
748 For integer C<isl_val>s we additionally have the following binary property.
751 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
752 __isl_keep isl_val *v2);
754 An C<isl_val> can also be compared to an integer using the following
755 functions. The result of C<isl_val_cmp_si> undefined for NaN.
758 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
759 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
761 The following unary operations are available on C<isl_val>s.
764 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
765 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
766 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
767 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
768 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
769 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
770 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
772 The following binary operations are available on C<isl_val>s.
775 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
776 __isl_take isl_val *v2);
777 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
778 __isl_take isl_val *v2);
779 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
780 __isl_take isl_val *v2);
781 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
783 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
784 __isl_take isl_val *v2);
785 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
787 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
788 __isl_take isl_val *v2);
789 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
791 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
792 __isl_take isl_val *v2);
793 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
796 On integer values, we additionally have the following operations.
799 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
800 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
801 __isl_take isl_val *v2);
802 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
803 __isl_take isl_val *v2);
804 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
805 __isl_take isl_val *v2, __isl_give isl_val **x,
806 __isl_give isl_val **y);
808 The function C<isl_val_gcdext> returns the greatest common divisor g
809 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
810 that C<*x> * C<v1> + C<*y> * C<v2> = g.
812 =head3 GMP specific functions
814 These functions are only available if C<isl> has been compiled with C<GMP>
817 Specific integer and rational values can be created from C<GMP> values using
818 the following functions.
820 #include <isl/val_gmp.h>
821 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
823 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
824 const mpz_t n, const mpz_t d);
826 The numerator and denominator of a rational value can be extracted as
827 C<GMP> values using the following functions.
829 #include <isl/val_gmp.h>
830 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
831 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
833 =head2 Sets and Relations
835 C<isl> uses six types of objects for representing sets and relations,
836 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
837 C<isl_union_set> and C<isl_union_map>.
838 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
839 can be described as a conjunction of affine constraints, while
840 C<isl_set> and C<isl_map> represent unions of
841 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
842 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
843 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
844 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
845 where spaces are considered different if they have a different number
846 of dimensions and/or different names (see L<"Spaces">).
847 The difference between sets and relations (maps) is that sets have
848 one set of variables, while relations have two sets of variables,
849 input variables and output variables.
851 =head2 Error Handling
853 C<isl> supports different ways to react in case a runtime error is triggered.
854 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
855 with two maps that have incompatible spaces. There are three possible ways
856 to react on error: to warn, to continue or to abort.
858 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
859 the last error in the corresponding C<isl_ctx> and the function in which the
860 error was triggered returns a value indicating that some error has
861 occurred. In case of functions returning a pointer, this value is
862 C<NULL>. In case of functions returning an C<isl_bool> or an
863 C<isl_stat>, this value is C<isl_bool_error> or C<isl_stat_error>.
864 An error does not corrupt internal state,
865 such that isl can continue to be used. C<isl> also provides functions to
866 read the last error, including the specific error message,
867 the isl source file where the error occurred and the line number,
868 and to reset all information about the last error. The
869 last error is only stored for information purposes. Its presence does not
870 change the behavior of C<isl>. Hence, resetting an error is not required to
871 continue to use isl, but only to observe new errors.
874 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
875 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
876 const char *isl_ctx_last_error_file(isl_ctx *ctx);
877 int isl_ctx_last_error_line(isl_ctx *ctx);
878 void isl_ctx_reset_error(isl_ctx *ctx);
880 If no error has occurred since the last call to C<isl_ctx_reset_error>,
881 then the functions C<isl_ctx_last_error_msg> and
882 C<isl_ctx_last_error_file> return C<NULL>.
884 Another option is to continue on error. This is similar to warn on error mode,
885 except that C<isl> does not print any warning. This allows a program to
886 implement its own error reporting.
888 The last option is to directly abort the execution of the program from within
889 the isl library. This makes it obviously impossible to recover from an error,
890 but it allows to directly spot the error location. By aborting on error,
891 debuggers break at the location the error occurred and can provide a stack
892 trace. Other tools that automatically provide stack traces on abort or that do
893 not want to continue execution after an error was triggered may also prefer to
896 The on error behavior of isl can be specified by calling
897 C<isl_options_set_on_error> or by setting the command line option
898 C<--isl-on-error>. Valid arguments for the function call are
899 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
900 choices for the command line option are C<warn>, C<continue> and C<abort>.
901 It is also possible to query the current error mode.
903 #include <isl/options.h>
904 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
905 int isl_options_get_on_error(isl_ctx *ctx);
909 Identifiers are used to identify both individual dimensions
910 and tuples of dimensions. They consist of an optional name and an optional
911 user pointer. The name and the user pointer cannot both be C<NULL>, however.
912 Identifiers with the same name but different pointer values
913 are considered to be distinct.
914 Similarly, identifiers with different names but the same pointer value
915 are also considered to be distinct.
916 Equal identifiers are represented using the same object.
917 Pairs of identifiers can therefore be tested for equality using the
919 Identifiers can be constructed, copied, freed, inspected and printed
920 using the following functions.
923 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
924 __isl_keep const char *name, void *user);
925 __isl_give isl_id *isl_id_set_free_user(
926 __isl_take isl_id *id,
927 void (*free_user)(void *user));
928 __isl_give isl_id *isl_id_copy(isl_id *id);
929 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
931 void *isl_id_get_user(__isl_keep isl_id *id);
932 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
934 __isl_give isl_printer *isl_printer_print_id(
935 __isl_take isl_printer *p, __isl_keep isl_id *id);
937 The callback set by C<isl_id_set_free_user> is called on the user
938 pointer when the last reference to the C<isl_id> is freed.
939 Note that C<isl_id_get_name> returns a pointer to some internal
940 data structure, so the result can only be used while the
941 corresponding C<isl_id> is alive.
945 Whenever a new set, relation or similar object is created from scratch,
946 the space in which it lives needs to be specified using an C<isl_space>.
947 Each space involves zero or more parameters and zero, one or two
948 tuples of set or input/output dimensions. The parameters and dimensions
949 are identified by an C<isl_dim_type> and a position.
950 The type C<isl_dim_param> refers to parameters,
951 the type C<isl_dim_set> refers to set dimensions (for spaces
952 with a single tuple of dimensions) and the types C<isl_dim_in>
953 and C<isl_dim_out> refer to input and output dimensions
954 (for spaces with two tuples of dimensions).
955 Local spaces (see L</"Local Spaces">) also contain dimensions
956 of type C<isl_dim_div>.
957 Note that parameters are only identified by their position within
958 a given object. Across different objects, parameters are (usually)
959 identified by their names or identifiers. Only unnamed parameters
960 are identified by their positions across objects. The use of unnamed
961 parameters is discouraged.
963 #include <isl/space.h>
964 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
965 unsigned nparam, unsigned n_in, unsigned n_out);
966 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
968 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
969 unsigned nparam, unsigned dim);
970 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
971 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
973 The space used for creating a parameter domain
974 needs to be created using C<isl_space_params_alloc>.
975 For other sets, the space
976 needs to be created using C<isl_space_set_alloc>, while
977 for a relation, the space
978 needs to be created using C<isl_space_alloc>.
980 To check whether a given space is that of a set or a map
981 or whether it is a parameter space, use these functions:
983 #include <isl/space.h>
984 isl_bool isl_space_is_params(__isl_keep isl_space *space);
985 isl_bool isl_space_is_set(__isl_keep isl_space *space);
986 isl_bool isl_space_is_map(__isl_keep isl_space *space);
988 Spaces can be compared using the following functions:
990 #include <isl/space.h>
991 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
992 __isl_keep isl_space *space2);
993 isl_bool isl_space_has_equal_params(
994 __isl_keep isl_space *space1,
995 __isl_keep isl_space *space2);
996 isl_bool isl_space_has_equal_tuples(
997 __isl_keep isl_space *space1,
998 __isl_keep isl_space *space2);
999 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
1000 __isl_keep isl_space *space2);
1001 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
1002 __isl_keep isl_space *space2);
1003 isl_bool isl_space_tuple_is_equal(
1004 __isl_keep isl_space *space1,
1005 enum isl_dim_type type1,
1006 __isl_keep isl_space *space2,
1007 enum isl_dim_type type2);
1009 C<isl_space_is_domain> checks whether the first argument is equal
1010 to the domain of the second argument. This requires in particular that
1011 the first argument is a set space and that the second argument
1012 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1013 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1014 spaces are the same. That is, it checks if they have the same
1015 identifier (if any), the same dimension and the same internal structure
1018 C<isl_space_has_equal_params> checks whether two spaces
1019 have the same parameters in the same order.
1020 C<isl_space_has_equal_tuples> check whether two spaces have
1021 the same tuples. In contrast to C<isl_space_is_equal> below,
1022 it does not check the
1023 parameters. This is useful because many C<isl> functions align the
1024 parameters before they perform their operations, such that equivalence
1026 C<isl_space_is_equal> checks whether two spaces are identical,
1027 meaning that they have the same parameters and the same tuples.
1028 That is, it checks whether both C<isl_space_has_equal_params> and
1029 C<isl_space_has_equal_tuples> hold.
1031 It is often useful to create objects that live in the
1032 same space as some other object. This can be accomplished
1033 by creating the new objects
1034 (see L</"Creating New Sets and Relations"> or
1035 L</"Functions">) based on the space
1036 of the original object.
1038 #include <isl/set.h>
1039 __isl_give isl_space *isl_basic_set_get_space(
1040 __isl_keep isl_basic_set *bset);
1041 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1043 #include <isl/union_set.h>
1044 __isl_give isl_space *isl_union_set_get_space(
1045 __isl_keep isl_union_set *uset);
1047 #include <isl/map.h>
1048 __isl_give isl_space *isl_basic_map_get_space(
1049 __isl_keep isl_basic_map *bmap);
1050 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1052 #include <isl/union_map.h>
1053 __isl_give isl_space *isl_union_map_get_space(
1054 __isl_keep isl_union_map *umap);
1056 #include <isl/constraint.h>
1057 __isl_give isl_space *isl_constraint_get_space(
1058 __isl_keep isl_constraint *constraint);
1060 #include <isl/polynomial.h>
1061 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1062 __isl_keep isl_qpolynomial *qp);
1063 __isl_give isl_space *isl_qpolynomial_get_space(
1064 __isl_keep isl_qpolynomial *qp);
1065 __isl_give isl_space *
1066 isl_qpolynomial_fold_get_domain_space(
1067 __isl_keep isl_qpolynomial_fold *fold);
1068 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1069 __isl_keep isl_qpolynomial_fold *fold);
1070 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1071 __isl_keep isl_pw_qpolynomial *pwqp);
1072 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1073 __isl_keep isl_pw_qpolynomial *pwqp);
1074 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1075 __isl_keep isl_pw_qpolynomial_fold *pwf);
1076 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1077 __isl_keep isl_pw_qpolynomial_fold *pwf);
1078 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1079 __isl_keep isl_union_pw_qpolynomial *upwqp);
1080 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1081 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1083 #include <isl/val.h>
1084 __isl_give isl_space *isl_multi_val_get_space(
1085 __isl_keep isl_multi_val *mv);
1087 #include <isl/aff.h>
1088 __isl_give isl_space *isl_aff_get_domain_space(
1089 __isl_keep isl_aff *aff);
1090 __isl_give isl_space *isl_aff_get_space(
1091 __isl_keep isl_aff *aff);
1092 __isl_give isl_space *isl_pw_aff_get_domain_space(
1093 __isl_keep isl_pw_aff *pwaff);
1094 __isl_give isl_space *isl_pw_aff_get_space(
1095 __isl_keep isl_pw_aff *pwaff);
1096 __isl_give isl_space *isl_multi_aff_get_domain_space(
1097 __isl_keep isl_multi_aff *maff);
1098 __isl_give isl_space *isl_multi_aff_get_space(
1099 __isl_keep isl_multi_aff *maff);
1100 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1101 __isl_keep isl_pw_multi_aff *pma);
1102 __isl_give isl_space *isl_pw_multi_aff_get_space(
1103 __isl_keep isl_pw_multi_aff *pma);
1104 __isl_give isl_space *isl_union_pw_aff_get_space(
1105 __isl_keep isl_union_pw_aff *upa);
1106 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1107 __isl_keep isl_union_pw_multi_aff *upma);
1108 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1109 __isl_keep isl_multi_pw_aff *mpa);
1110 __isl_give isl_space *isl_multi_pw_aff_get_space(
1111 __isl_keep isl_multi_pw_aff *mpa);
1112 __isl_give isl_space *
1113 isl_multi_union_pw_aff_get_domain_space(
1114 __isl_keep isl_multi_union_pw_aff *mupa);
1115 __isl_give isl_space *
1116 isl_multi_union_pw_aff_get_space(
1117 __isl_keep isl_multi_union_pw_aff *mupa);
1119 #include <isl/point.h>
1120 __isl_give isl_space *isl_point_get_space(
1121 __isl_keep isl_point *pnt);
1123 #include <isl/fixed_box.h>
1124 __isl_give isl_space *isl_fixed_box_get_space(
1125 __isl_keep isl_fixed_box *box);
1127 The number of dimensions of a given type of space
1128 may be read off from a space or an object that lives
1129 in a space using the following functions.
1130 In case of C<isl_space_dim>, type may be
1131 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1132 C<isl_dim_out> (only for relations), C<isl_dim_set>
1133 (only for sets) or C<isl_dim_all>.
1135 #include <isl/space.h>
1136 unsigned isl_space_dim(__isl_keep isl_space *space,
1137 enum isl_dim_type type);
1139 #include <isl/local_space.h>
1140 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1141 enum isl_dim_type type);
1143 #include <isl/set.h>
1144 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1145 enum isl_dim_type type);
1146 unsigned isl_set_dim(__isl_keep isl_set *set,
1147 enum isl_dim_type type);
1149 #include <isl/union_set.h>
1150 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1151 enum isl_dim_type type);
1153 #include <isl/map.h>
1154 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1155 enum isl_dim_type type);
1156 unsigned isl_map_dim(__isl_keep isl_map *map,
1157 enum isl_dim_type type);
1159 #include <isl/union_map.h>
1160 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1161 enum isl_dim_type type);
1163 #include <isl/val.h>
1164 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1165 enum isl_dim_type type);
1167 #include <isl/aff.h>
1168 int isl_aff_dim(__isl_keep isl_aff *aff,
1169 enum isl_dim_type type);
1170 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1171 enum isl_dim_type type);
1172 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1173 enum isl_dim_type type);
1174 unsigned isl_pw_multi_aff_dim(
1175 __isl_keep isl_pw_multi_aff *pma,
1176 enum isl_dim_type type);
1177 unsigned isl_multi_pw_aff_dim(
1178 __isl_keep isl_multi_pw_aff *mpa,
1179 enum isl_dim_type type);
1180 unsigned isl_union_pw_aff_dim(
1181 __isl_keep isl_union_pw_aff *upa,
1182 enum isl_dim_type type);
1183 unsigned isl_union_pw_multi_aff_dim(
1184 __isl_keep isl_union_pw_multi_aff *upma,
1185 enum isl_dim_type type);
1186 unsigned isl_multi_union_pw_aff_dim(
1187 __isl_keep isl_multi_union_pw_aff *mupa,
1188 enum isl_dim_type type);
1190 #include <isl/polynomial.h>
1191 unsigned isl_union_pw_qpolynomial_dim(
1192 __isl_keep isl_union_pw_qpolynomial *upwqp,
1193 enum isl_dim_type type);
1194 unsigned isl_union_pw_qpolynomial_fold_dim(
1195 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1196 enum isl_dim_type type);
1198 Note that an C<isl_union_set>, an C<isl_union_map>,
1199 an C<isl_union_pw_multi_aff>,
1200 an C<isl_union_pw_qpolynomial> and
1201 an C<isl_union_pw_qpolynomial_fold>
1202 only have parameters.
1204 Additional parameters can be added to a space using the following function.
1206 #include <isl/space.h>
1207 __isl_give isl_space *isl_space_add_param_id(
1208 __isl_take isl_space *space,
1209 __isl_take isl_id *id);
1211 If a parameter with the given identifier already appears in the space,
1212 then it is not added again.
1214 The identifiers or names of the individual dimensions of spaces
1215 may be set or read off using the following functions on spaces
1216 or objects that live in spaces.
1217 These functions are mostly useful to obtain the identifiers, positions
1218 or names of the parameters. Identifiers of individual dimensions are
1219 essentially only useful for printing. They are ignored by all other
1220 operations and may not be preserved across those operations.
1222 #include <isl/space.h>
1223 __isl_give isl_space *isl_space_set_dim_id(
1224 __isl_take isl_space *space,
1225 enum isl_dim_type type, unsigned pos,
1226 __isl_take isl_id *id);
1227 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1228 enum isl_dim_type type, unsigned pos);
1229 __isl_give isl_id *isl_space_get_dim_id(
1230 __isl_keep isl_space *space,
1231 enum isl_dim_type type, unsigned pos);
1232 __isl_give isl_space *isl_space_set_dim_name(
1233 __isl_take isl_space *space,
1234 enum isl_dim_type type, unsigned pos,
1235 __isl_keep const char *name);
1236 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1237 enum isl_dim_type type, unsigned pos);
1238 __isl_keep const char *isl_space_get_dim_name(
1239 __isl_keep isl_space *space,
1240 enum isl_dim_type type, unsigned pos);
1242 #include <isl/local_space.h>
1243 __isl_give isl_local_space *isl_local_space_set_dim_id(
1244 __isl_take isl_local_space *ls,
1245 enum isl_dim_type type, unsigned pos,
1246 __isl_take isl_id *id);
1247 isl_bool isl_local_space_has_dim_id(
1248 __isl_keep isl_local_space *ls,
1249 enum isl_dim_type type, unsigned pos);
1250 __isl_give isl_id *isl_local_space_get_dim_id(
1251 __isl_keep isl_local_space *ls,
1252 enum isl_dim_type type, unsigned pos);
1253 __isl_give isl_local_space *isl_local_space_set_dim_name(
1254 __isl_take isl_local_space *ls,
1255 enum isl_dim_type type, unsigned pos, const char *s);
1256 isl_bool isl_local_space_has_dim_name(
1257 __isl_keep isl_local_space *ls,
1258 enum isl_dim_type type, unsigned pos)
1259 const char *isl_local_space_get_dim_name(
1260 __isl_keep isl_local_space *ls,
1261 enum isl_dim_type type, unsigned pos);
1263 #include <isl/constraint.h>
1264 const char *isl_constraint_get_dim_name(
1265 __isl_keep isl_constraint *constraint,
1266 enum isl_dim_type type, unsigned pos);
1268 #include <isl/set.h>
1269 __isl_give isl_id *isl_basic_set_get_dim_id(
1270 __isl_keep isl_basic_set *bset,
1271 enum isl_dim_type type, unsigned pos);
1272 __isl_give isl_set *isl_set_set_dim_id(
1273 __isl_take isl_set *set, enum isl_dim_type type,
1274 unsigned pos, __isl_take isl_id *id);
1275 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1276 enum isl_dim_type type, unsigned pos);
1277 __isl_give isl_id *isl_set_get_dim_id(
1278 __isl_keep isl_set *set, enum isl_dim_type type,
1280 const char *isl_basic_set_get_dim_name(
1281 __isl_keep isl_basic_set *bset,
1282 enum isl_dim_type type, unsigned pos);
1283 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1284 enum isl_dim_type type, unsigned pos);
1285 const char *isl_set_get_dim_name(
1286 __isl_keep isl_set *set,
1287 enum isl_dim_type type, unsigned pos);
1289 #include <isl/map.h>
1290 __isl_give isl_map *isl_map_set_dim_id(
1291 __isl_take isl_map *map, enum isl_dim_type type,
1292 unsigned pos, __isl_take isl_id *id);
1293 isl_bool isl_basic_map_has_dim_id(
1294 __isl_keep isl_basic_map *bmap,
1295 enum isl_dim_type type, unsigned pos);
1296 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1297 enum isl_dim_type type, unsigned pos);
1298 __isl_give isl_id *isl_map_get_dim_id(
1299 __isl_keep isl_map *map, enum isl_dim_type type,
1301 __isl_give isl_id *isl_union_map_get_dim_id(
1302 __isl_keep isl_union_map *umap,
1303 enum isl_dim_type type, unsigned pos);
1304 const char *isl_basic_map_get_dim_name(
1305 __isl_keep isl_basic_map *bmap,
1306 enum isl_dim_type type, unsigned pos);
1307 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1308 enum isl_dim_type type, unsigned pos);
1309 const char *isl_map_get_dim_name(
1310 __isl_keep isl_map *map,
1311 enum isl_dim_type type, unsigned pos);
1313 #include <isl/val.h>
1314 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1315 __isl_take isl_multi_val *mv,
1316 enum isl_dim_type type, unsigned pos,
1317 __isl_take isl_id *id);
1318 __isl_give isl_id *isl_multi_val_get_dim_id(
1319 __isl_keep isl_multi_val *mv,
1320 enum isl_dim_type type, unsigned pos);
1321 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1322 __isl_take isl_multi_val *mv,
1323 enum isl_dim_type type, unsigned pos, const char *s);
1325 #include <isl/aff.h>
1326 __isl_give isl_aff *isl_aff_set_dim_id(
1327 __isl_take isl_aff *aff, enum isl_dim_type type,
1328 unsigned pos, __isl_take isl_id *id);
1329 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1330 __isl_take isl_multi_aff *maff,
1331 enum isl_dim_type type, unsigned pos,
1332 __isl_take isl_id *id);
1333 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1334 __isl_take isl_pw_aff *pma,
1335 enum isl_dim_type type, unsigned pos,
1336 __isl_take isl_id *id);
1337 __isl_give isl_multi_pw_aff *
1338 isl_multi_pw_aff_set_dim_id(
1339 __isl_take isl_multi_pw_aff *mpa,
1340 enum isl_dim_type type, unsigned pos,
1341 __isl_take isl_id *id);
1342 __isl_give isl_multi_union_pw_aff *
1343 isl_multi_union_pw_aff_set_dim_id(
1344 __isl_take isl_multi_union_pw_aff *mupa,
1345 enum isl_dim_type type, unsigned pos,
1346 __isl_take isl_id *id);
1347 __isl_give isl_id *isl_multi_aff_get_dim_id(
1348 __isl_keep isl_multi_aff *ma,
1349 enum isl_dim_type type, unsigned pos);
1350 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1351 enum isl_dim_type type, unsigned pos);
1352 __isl_give isl_id *isl_pw_aff_get_dim_id(
1353 __isl_keep isl_pw_aff *pa,
1354 enum isl_dim_type type, unsigned pos);
1355 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1356 __isl_keep isl_pw_multi_aff *pma,
1357 enum isl_dim_type type, unsigned pos);
1358 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1359 __isl_keep isl_multi_pw_aff *mpa,
1360 enum isl_dim_type type, unsigned pos);
1361 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1362 __isl_keep isl_multi_union_pw_aff *mupa,
1363 enum isl_dim_type type, unsigned pos);
1364 __isl_give isl_aff *isl_aff_set_dim_name(
1365 __isl_take isl_aff *aff, enum isl_dim_type type,
1366 unsigned pos, const char *s);
1367 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1368 __isl_take isl_multi_aff *maff,
1369 enum isl_dim_type type, unsigned pos, const char *s);
1370 __isl_give isl_multi_pw_aff *
1371 isl_multi_pw_aff_set_dim_name(
1372 __isl_take isl_multi_pw_aff *mpa,
1373 enum isl_dim_type type, unsigned pos, const char *s);
1374 __isl_give isl_union_pw_aff *
1375 isl_union_pw_aff_set_dim_name(
1376 __isl_take isl_union_pw_aff *upa,
1377 enum isl_dim_type type, unsigned pos,
1379 __isl_give isl_union_pw_multi_aff *
1380 isl_union_pw_multi_aff_set_dim_name(
1381 __isl_take isl_union_pw_multi_aff *upma,
1382 enum isl_dim_type type, unsigned pos,
1384 __isl_give isl_multi_union_pw_aff *
1385 isl_multi_union_pw_aff_set_dim_name(
1386 __isl_take isl_multi_union_pw_aff *mupa,
1387 enum isl_dim_type type, unsigned pos,
1388 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1389 enum isl_dim_type type, unsigned pos);
1390 const char *isl_pw_aff_get_dim_name(
1391 __isl_keep isl_pw_aff *pa,
1392 enum isl_dim_type type, unsigned pos);
1393 const char *isl_pw_multi_aff_get_dim_name(
1394 __isl_keep isl_pw_multi_aff *pma,
1395 enum isl_dim_type type, unsigned pos);
1397 #include <isl/polynomial.h>
1398 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1399 __isl_take isl_qpolynomial *qp,
1400 enum isl_dim_type type, unsigned pos,
1402 __isl_give isl_pw_qpolynomial *
1403 isl_pw_qpolynomial_set_dim_name(
1404 __isl_take isl_pw_qpolynomial *pwqp,
1405 enum isl_dim_type type, unsigned pos,
1407 __isl_give isl_pw_qpolynomial_fold *
1408 isl_pw_qpolynomial_fold_set_dim_name(
1409 __isl_take isl_pw_qpolynomial_fold *pwf,
1410 enum isl_dim_type type, unsigned pos,
1412 __isl_give isl_union_pw_qpolynomial *
1413 isl_union_pw_qpolynomial_set_dim_name(
1414 __isl_take isl_union_pw_qpolynomial *upwqp,
1415 enum isl_dim_type type, unsigned pos,
1417 __isl_give isl_union_pw_qpolynomial_fold *
1418 isl_union_pw_qpolynomial_fold_set_dim_name(
1419 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1420 enum isl_dim_type type, unsigned pos,
1423 Note that C<isl_space_get_name> returns a pointer to some internal
1424 data structure, so the result can only be used while the
1425 corresponding C<isl_space> is alive.
1426 Also note that every function that operates on two sets or relations
1427 requires that both arguments have the same parameters. This also
1428 means that if one of the arguments has named parameters, then the
1429 other needs to have named parameters too and the names need to match.
1430 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1431 arguments may have different parameters (as long as they are named),
1432 in which case the result will have as parameters the union of the parameters of
1435 Given the identifier or name of a dimension (typically a parameter),
1436 its position can be obtained from the following functions.
1438 #include <isl/space.h>
1439 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1440 enum isl_dim_type type, __isl_keep isl_id *id);
1441 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1442 enum isl_dim_type type, const char *name);
1444 #include <isl/local_space.h>
1445 int isl_local_space_find_dim_by_name(
1446 __isl_keep isl_local_space *ls,
1447 enum isl_dim_type type, const char *name);
1449 #include <isl/val.h>
1450 int isl_multi_val_find_dim_by_id(
1451 __isl_keep isl_multi_val *mv,
1452 enum isl_dim_type type, __isl_keep isl_id *id);
1453 int isl_multi_val_find_dim_by_name(
1454 __isl_keep isl_multi_val *mv,
1455 enum isl_dim_type type, const char *name);
1457 #include <isl/set.h>
1458 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1459 enum isl_dim_type type, __isl_keep isl_id *id);
1460 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1461 enum isl_dim_type type, const char *name);
1463 #include <isl/map.h>
1464 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1465 enum isl_dim_type type, __isl_keep isl_id *id);
1466 int isl_basic_map_find_dim_by_name(
1467 __isl_keep isl_basic_map *bmap,
1468 enum isl_dim_type type, const char *name);
1469 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1470 enum isl_dim_type type, const char *name);
1471 int isl_union_map_find_dim_by_name(
1472 __isl_keep isl_union_map *umap,
1473 enum isl_dim_type type, const char *name);
1475 #include <isl/aff.h>
1476 int isl_multi_aff_find_dim_by_id(
1477 __isl_keep isl_multi_aff *ma,
1478 enum isl_dim_type type, __isl_keep isl_id *id);
1479 int isl_multi_pw_aff_find_dim_by_id(
1480 __isl_keep isl_multi_pw_aff *mpa,
1481 enum isl_dim_type type, __isl_keep isl_id *id);
1482 int isl_multi_union_pw_aff_find_dim_by_id(
1483 __isl_keep isl_union_multi_pw_aff *mupa,
1484 enum isl_dim_type type, __isl_keep isl_id *id);
1485 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1486 enum isl_dim_type type, const char *name);
1487 int isl_multi_aff_find_dim_by_name(
1488 __isl_keep isl_multi_aff *ma,
1489 enum isl_dim_type type, const char *name);
1490 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1491 enum isl_dim_type type, const char *name);
1492 int isl_multi_pw_aff_find_dim_by_name(
1493 __isl_keep isl_multi_pw_aff *mpa,
1494 enum isl_dim_type type, const char *name);
1495 int isl_pw_multi_aff_find_dim_by_name(
1496 __isl_keep isl_pw_multi_aff *pma,
1497 enum isl_dim_type type, const char *name);
1498 int isl_union_pw_aff_find_dim_by_name(
1499 __isl_keep isl_union_pw_aff *upa,
1500 enum isl_dim_type type, const char *name);
1501 int isl_union_pw_multi_aff_find_dim_by_name(
1502 __isl_keep isl_union_pw_multi_aff *upma,
1503 enum isl_dim_type type, const char *name);
1504 int isl_multi_union_pw_aff_find_dim_by_name(
1505 __isl_keep isl_multi_union_pw_aff *mupa,
1506 enum isl_dim_type type, const char *name);
1508 #include <isl/polynomial.h>
1509 int isl_pw_qpolynomial_find_dim_by_name(
1510 __isl_keep isl_pw_qpolynomial *pwqp,
1511 enum isl_dim_type type, const char *name);
1512 int isl_pw_qpolynomial_fold_find_dim_by_name(
1513 __isl_keep isl_pw_qpolynomial_fold *pwf,
1514 enum isl_dim_type type, const char *name);
1515 int isl_union_pw_qpolynomial_find_dim_by_name(
1516 __isl_keep isl_union_pw_qpolynomial *upwqp,
1517 enum isl_dim_type type, const char *name);
1518 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1519 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1520 enum isl_dim_type type, const char *name);
1522 The identifiers or names of entire spaces may be set or read off
1523 using the following functions.
1525 #include <isl/space.h>
1526 __isl_give isl_space *isl_space_set_tuple_id(
1527 __isl_take isl_space *space,
1528 enum isl_dim_type type, __isl_take isl_id *id);
1529 __isl_give isl_space *isl_space_reset_tuple_id(
1530 __isl_take isl_space *space, enum isl_dim_type type);
1531 isl_bool isl_space_has_tuple_id(
1532 __isl_keep isl_space *space,
1533 enum isl_dim_type type);
1534 __isl_give isl_id *isl_space_get_tuple_id(
1535 __isl_keep isl_space *space, enum isl_dim_type type);
1536 __isl_give isl_space *isl_space_set_tuple_name(
1537 __isl_take isl_space *space,
1538 enum isl_dim_type type, const char *s);
1539 isl_bool isl_space_has_tuple_name(
1540 __isl_keep isl_space *space,
1541 enum isl_dim_type type);
1542 __isl_keep const char *isl_space_get_tuple_name(
1543 __isl_keep isl_space *space,
1544 enum isl_dim_type type);
1546 #include <isl/local_space.h>
1547 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1548 __isl_take isl_local_space *ls,
1549 enum isl_dim_type type, __isl_take isl_id *id);
1551 #include <isl/set.h>
1552 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1553 __isl_take isl_basic_set *bset,
1554 __isl_take isl_id *id);
1555 __isl_give isl_set *isl_set_set_tuple_id(
1556 __isl_take isl_set *set, __isl_take isl_id *id);
1557 __isl_give isl_set *isl_set_reset_tuple_id(
1558 __isl_take isl_set *set);
1559 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1560 __isl_give isl_id *isl_set_get_tuple_id(
1561 __isl_keep isl_set *set);
1562 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1563 __isl_take isl_basic_set *set, const char *s);
1564 __isl_give isl_set *isl_set_set_tuple_name(
1565 __isl_take isl_set *set, const char *s);
1566 const char *isl_basic_set_get_tuple_name(
1567 __isl_keep isl_basic_set *bset);
1568 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1569 const char *isl_set_get_tuple_name(
1570 __isl_keep isl_set *set);
1572 #include <isl/map.h>
1573 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1574 __isl_take isl_basic_map *bmap,
1575 enum isl_dim_type type, __isl_take isl_id *id);
1576 __isl_give isl_map *isl_map_set_tuple_id(
1577 __isl_take isl_map *map, enum isl_dim_type type,
1578 __isl_take isl_id *id);
1579 __isl_give isl_map *isl_map_reset_tuple_id(
1580 __isl_take isl_map *map, enum isl_dim_type type);
1581 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1582 enum isl_dim_type type);
1583 __isl_give isl_id *isl_map_get_tuple_id(
1584 __isl_keep isl_map *map, enum isl_dim_type type);
1585 __isl_give isl_map *isl_map_set_tuple_name(
1586 __isl_take isl_map *map,
1587 enum isl_dim_type type, const char *s);
1588 const char *isl_basic_map_get_tuple_name(
1589 __isl_keep isl_basic_map *bmap,
1590 enum isl_dim_type type);
1591 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1592 __isl_take isl_basic_map *bmap,
1593 enum isl_dim_type type, const char *s);
1594 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1595 enum isl_dim_type type);
1596 const char *isl_map_get_tuple_name(
1597 __isl_keep isl_map *map,
1598 enum isl_dim_type type);
1600 #include <isl/val.h>
1601 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1602 __isl_take isl_multi_val *mv,
1603 enum isl_dim_type type, __isl_take isl_id *id);
1604 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1605 __isl_take isl_multi_val *mv,
1606 enum isl_dim_type type);
1607 isl_bool isl_multi_val_has_tuple_id(
1608 __isl_keep isl_multi_val *mv,
1609 enum isl_dim_type type);
1610 __isl_give isl_id *isl_multi_val_get_tuple_id(
1611 __isl_keep isl_multi_val *mv,
1612 enum isl_dim_type type);
1613 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1614 __isl_take isl_multi_val *mv,
1615 enum isl_dim_type type, const char *s);
1616 const char *isl_multi_val_get_tuple_name(
1617 __isl_keep isl_multi_val *mv,
1618 enum isl_dim_type type);
1620 #include <isl/aff.h>
1621 __isl_give isl_aff *isl_aff_set_tuple_id(
1622 __isl_take isl_aff *aff,
1623 enum isl_dim_type type, __isl_take isl_id *id);
1624 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1625 __isl_take isl_multi_aff *maff,
1626 enum isl_dim_type type, __isl_take isl_id *id);
1627 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1628 __isl_take isl_pw_aff *pwaff,
1629 enum isl_dim_type type, __isl_take isl_id *id);
1630 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1631 __isl_take isl_pw_multi_aff *pma,
1632 enum isl_dim_type type, __isl_take isl_id *id);
1633 __isl_give isl_multi_union_pw_aff *
1634 isl_multi_union_pw_aff_set_tuple_id(
1635 __isl_take isl_multi_union_pw_aff *mupa,
1636 enum isl_dim_type type, __isl_take isl_id *id);
1637 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1638 __isl_take isl_multi_aff *ma,
1639 enum isl_dim_type type);
1640 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1641 __isl_take isl_pw_aff *pa,
1642 enum isl_dim_type type);
1643 __isl_give isl_multi_pw_aff *
1644 isl_multi_pw_aff_reset_tuple_id(
1645 __isl_take isl_multi_pw_aff *mpa,
1646 enum isl_dim_type type);
1647 __isl_give isl_pw_multi_aff *
1648 isl_pw_multi_aff_reset_tuple_id(
1649 __isl_take isl_pw_multi_aff *pma,
1650 enum isl_dim_type type);
1651 __isl_give isl_multi_union_pw_aff *
1652 isl_multi_union_pw_aff_reset_tuple_id(
1653 __isl_take isl_multi_union_pw_aff *mupa,
1654 enum isl_dim_type type);
1655 isl_bool isl_multi_aff_has_tuple_id(
1656 __isl_keep isl_multi_aff *ma,
1657 enum isl_dim_type type);
1658 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1659 __isl_keep isl_multi_aff *ma,
1660 enum isl_dim_type type);
1661 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1662 enum isl_dim_type type);
1663 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1664 __isl_keep isl_pw_aff *pa,
1665 enum isl_dim_type type);
1666 isl_bool isl_pw_multi_aff_has_tuple_id(
1667 __isl_keep isl_pw_multi_aff *pma,
1668 enum isl_dim_type type);
1669 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1670 __isl_keep isl_pw_multi_aff *pma,
1671 enum isl_dim_type type);
1672 isl_bool isl_multi_pw_aff_has_tuple_id(
1673 __isl_keep isl_multi_pw_aff *mpa,
1674 enum isl_dim_type type);
1675 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1676 __isl_keep isl_multi_pw_aff *mpa,
1677 enum isl_dim_type type);
1678 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1679 __isl_keep isl_multi_union_pw_aff *mupa,
1680 enum isl_dim_type type);
1681 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1682 __isl_keep isl_multi_union_pw_aff *mupa,
1683 enum isl_dim_type type);
1684 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1685 __isl_take isl_multi_aff *maff,
1686 enum isl_dim_type type, const char *s);
1687 __isl_give isl_multi_pw_aff *
1688 isl_multi_pw_aff_set_tuple_name(
1689 __isl_take isl_multi_pw_aff *mpa,
1690 enum isl_dim_type type, const char *s);
1691 __isl_give isl_multi_union_pw_aff *
1692 isl_multi_union_pw_aff_set_tuple_name(
1693 __isl_take isl_multi_union_pw_aff *mupa,
1694 enum isl_dim_type type, const char *s);
1695 const char *isl_multi_aff_get_tuple_name(
1696 __isl_keep isl_multi_aff *multi,
1697 enum isl_dim_type type);
1698 isl_bool isl_pw_multi_aff_has_tuple_name(
1699 __isl_keep isl_pw_multi_aff *pma,
1700 enum isl_dim_type type);
1701 const char *isl_pw_multi_aff_get_tuple_name(
1702 __isl_keep isl_pw_multi_aff *pma,
1703 enum isl_dim_type type);
1704 const char *isl_multi_union_pw_aff_get_tuple_name(
1705 __isl_keep isl_multi_union_pw_aff *mupa,
1706 enum isl_dim_type type);
1708 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1709 or C<isl_dim_set>. As with C<isl_space_get_name>,
1710 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1712 Binary operations require the corresponding spaces of their arguments
1713 to have the same name.
1715 To keep the names of all parameters and tuples, but reset the user pointers
1716 of all the corresponding identifiers, use the following function.
1718 #include <isl/space.h>
1719 __isl_give isl_space *isl_space_reset_user(
1720 __isl_take isl_space *space);
1722 #include <isl/set.h>
1723 __isl_give isl_set *isl_set_reset_user(
1724 __isl_take isl_set *set);
1726 #include <isl/map.h>
1727 __isl_give isl_map *isl_map_reset_user(
1728 __isl_take isl_map *map);
1730 #include <isl/union_set.h>
1731 __isl_give isl_union_set *isl_union_set_reset_user(
1732 __isl_take isl_union_set *uset);
1734 #include <isl/union_map.h>
1735 __isl_give isl_union_map *isl_union_map_reset_user(
1736 __isl_take isl_union_map *umap);
1738 #include <isl/val.h>
1739 __isl_give isl_multi_val *isl_multi_val_reset_user(
1740 __isl_take isl_multi_val *mv);
1742 #include <isl/aff.h>
1743 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1744 __isl_take isl_multi_aff *ma);
1745 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1746 __isl_take isl_pw_aff *pa);
1747 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1748 __isl_take isl_multi_pw_aff *mpa);
1749 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1750 __isl_take isl_pw_multi_aff *pma);
1751 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1752 __isl_take isl_union_pw_aff *upa);
1753 __isl_give isl_multi_union_pw_aff *
1754 isl_multi_union_pw_aff_reset_user(
1755 __isl_take isl_multi_union_pw_aff *mupa);
1756 __isl_give isl_union_pw_multi_aff *
1757 isl_union_pw_multi_aff_reset_user(
1758 __isl_take isl_union_pw_multi_aff *upma);
1760 #include <isl/polynomial.h>
1761 __isl_give isl_pw_qpolynomial *
1762 isl_pw_qpolynomial_reset_user(
1763 __isl_take isl_pw_qpolynomial *pwqp);
1764 __isl_give isl_union_pw_qpolynomial *
1765 isl_union_pw_qpolynomial_reset_user(
1766 __isl_take isl_union_pw_qpolynomial *upwqp);
1767 __isl_give isl_pw_qpolynomial_fold *
1768 isl_pw_qpolynomial_fold_reset_user(
1769 __isl_take isl_pw_qpolynomial_fold *pwf);
1770 __isl_give isl_union_pw_qpolynomial_fold *
1771 isl_union_pw_qpolynomial_fold_reset_user(
1772 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1774 Spaces can be nested. In particular, the domain of a set or
1775 the domain or range of a relation can be a nested relation.
1776 This process is also called I<wrapping>.
1777 The functions for detecting, constructing and deconstructing
1778 such nested spaces can be found in the wrapping properties
1779 of L</"Unary Properties">, the wrapping operations
1780 of L</"Unary Operations"> and the Cartesian product operations
1781 of L</"Basic Operations">.
1783 Spaces can be created from other spaces
1784 using the functions described in L</"Unary Operations">
1785 and L</"Binary Operations">.
1789 A local space is essentially a space with
1790 zero or more existentially quantified variables.
1791 The local space of various objects can be obtained
1792 using the following functions.
1794 #include <isl/constraint.h>
1795 __isl_give isl_local_space *isl_constraint_get_local_space(
1796 __isl_keep isl_constraint *constraint);
1798 #include <isl/set.h>
1799 __isl_give isl_local_space *isl_basic_set_get_local_space(
1800 __isl_keep isl_basic_set *bset);
1802 #include <isl/map.h>
1803 __isl_give isl_local_space *isl_basic_map_get_local_space(
1804 __isl_keep isl_basic_map *bmap);
1806 #include <isl/aff.h>
1807 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1808 __isl_keep isl_aff *aff);
1809 __isl_give isl_local_space *isl_aff_get_local_space(
1810 __isl_keep isl_aff *aff);
1812 A new local space can be created from a space using
1814 #include <isl/local_space.h>
1815 __isl_give isl_local_space *isl_local_space_from_space(
1816 __isl_take isl_space *space);
1818 They can be inspected, modified, copied and freed using the following functions.
1820 #include <isl/local_space.h>
1821 isl_bool isl_local_space_is_params(
1822 __isl_keep isl_local_space *ls);
1823 isl_bool isl_local_space_is_set(
1824 __isl_keep isl_local_space *ls);
1825 __isl_give isl_space *isl_local_space_get_space(
1826 __isl_keep isl_local_space *ls);
1827 __isl_give isl_aff *isl_local_space_get_div(
1828 __isl_keep isl_local_space *ls, int pos);
1829 __isl_give isl_local_space *isl_local_space_copy(
1830 __isl_keep isl_local_space *ls);
1831 __isl_null isl_local_space *isl_local_space_free(
1832 __isl_take isl_local_space *ls);
1834 Note that C<isl_local_space_get_div> can only be used on local spaces
1837 Two local spaces can be compared using
1839 isl_bool isl_local_space_is_equal(
1840 __isl_keep isl_local_space *ls1,
1841 __isl_keep isl_local_space *ls2);
1843 Local spaces can be created from other local spaces
1844 using the functions described in L</"Unary Operations">
1845 and L</"Binary Operations">.
1847 =head2 Creating New Sets and Relations
1849 C<isl> has functions for creating some standard sets and relations.
1853 =item * Empty sets and relations
1855 __isl_give isl_basic_set *isl_basic_set_empty(
1856 __isl_take isl_space *space);
1857 __isl_give isl_basic_map *isl_basic_map_empty(
1858 __isl_take isl_space *space);
1859 __isl_give isl_set *isl_set_empty(
1860 __isl_take isl_space *space);
1861 __isl_give isl_map *isl_map_empty(
1862 __isl_take isl_space *space);
1863 __isl_give isl_union_set *isl_union_set_empty(
1864 __isl_take isl_space *space);
1865 __isl_give isl_union_map *isl_union_map_empty(
1866 __isl_take isl_space *space);
1868 For C<isl_union_set>s and C<isl_union_map>s, the space
1869 is only used to specify the parameters.
1871 =item * Universe sets and relations
1873 __isl_give isl_basic_set *isl_basic_set_universe(
1874 __isl_take isl_space *space);
1875 __isl_give isl_basic_map *isl_basic_map_universe(
1876 __isl_take isl_space *space);
1877 __isl_give isl_set *isl_set_universe(
1878 __isl_take isl_space *space);
1879 __isl_give isl_map *isl_map_universe(
1880 __isl_take isl_space *space);
1881 __isl_give isl_union_set *isl_union_set_universe(
1882 __isl_take isl_union_set *uset);
1883 __isl_give isl_union_map *isl_union_map_universe(
1884 __isl_take isl_union_map *umap);
1886 The sets and relations constructed by the functions above
1887 contain all integer values, while those constructed by the
1888 functions below only contain non-negative values.
1890 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1891 __isl_take isl_space *space);
1892 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1893 __isl_take isl_space *space);
1894 __isl_give isl_set *isl_set_nat_universe(
1895 __isl_take isl_space *space);
1896 __isl_give isl_map *isl_map_nat_universe(
1897 __isl_take isl_space *space);
1899 =item * Identity relations
1901 __isl_give isl_basic_map *isl_basic_map_identity(
1902 __isl_take isl_space *space);
1903 __isl_give isl_map *isl_map_identity(
1904 __isl_take isl_space *space);
1906 The number of input and output dimensions in C<space> needs
1909 =item * Lexicographic order
1911 __isl_give isl_map *isl_map_lex_lt(
1912 __isl_take isl_space *set_space);
1913 __isl_give isl_map *isl_map_lex_le(
1914 __isl_take isl_space *set_space);
1915 __isl_give isl_map *isl_map_lex_gt(
1916 __isl_take isl_space *set_space);
1917 __isl_give isl_map *isl_map_lex_ge(
1918 __isl_take isl_space *set_space);
1919 __isl_give isl_map *isl_map_lex_lt_first(
1920 __isl_take isl_space *space, unsigned n);
1921 __isl_give isl_map *isl_map_lex_le_first(
1922 __isl_take isl_space *space, unsigned n);
1923 __isl_give isl_map *isl_map_lex_gt_first(
1924 __isl_take isl_space *space, unsigned n);
1925 __isl_give isl_map *isl_map_lex_ge_first(
1926 __isl_take isl_space *space, unsigned n);
1928 The first four functions take a space for a B<set>
1929 and return relations that express that the elements in the domain
1930 are lexicographically less
1931 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1932 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1933 than the elements in the range.
1934 The last four functions take a space for a map
1935 and return relations that express that the first C<n> dimensions
1936 in the domain are lexicographically less
1937 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1938 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1939 than the first C<n> dimensions in the range.
1943 A basic set or relation can be converted to a set or relation
1944 using the following functions.
1946 __isl_give isl_set *isl_set_from_basic_set(
1947 __isl_take isl_basic_set *bset);
1948 __isl_give isl_map *isl_map_from_basic_map(
1949 __isl_take isl_basic_map *bmap);
1951 Sets and relations can be converted to union sets and relations
1952 using the following functions.
1954 __isl_give isl_union_set *isl_union_set_from_basic_set(
1955 __isl_take isl_basic_set *bset);
1956 __isl_give isl_union_map *isl_union_map_from_basic_map(
1957 __isl_take isl_basic_map *bmap);
1958 __isl_give isl_union_set *isl_union_set_from_set(
1959 __isl_take isl_set *set);
1960 __isl_give isl_union_map *isl_union_map_from_map(
1961 __isl_take isl_map *map);
1963 The inverse conversions below can only be used if the input
1964 union set or relation is known to contain elements in exactly one
1967 __isl_give isl_set *isl_set_from_union_set(
1968 __isl_take isl_union_set *uset);
1969 __isl_give isl_map *isl_map_from_union_map(
1970 __isl_take isl_union_map *umap);
1972 Sets and relations can be copied and freed again using the following
1975 __isl_give isl_basic_set *isl_basic_set_copy(
1976 __isl_keep isl_basic_set *bset);
1977 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1978 __isl_give isl_union_set *isl_union_set_copy(
1979 __isl_keep isl_union_set *uset);
1980 __isl_give isl_basic_map *isl_basic_map_copy(
1981 __isl_keep isl_basic_map *bmap);
1982 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1983 __isl_give isl_union_map *isl_union_map_copy(
1984 __isl_keep isl_union_map *umap);
1985 __isl_null isl_basic_set *isl_basic_set_free(
1986 __isl_take isl_basic_set *bset);
1987 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1988 __isl_null isl_union_set *isl_union_set_free(
1989 __isl_take isl_union_set *uset);
1990 __isl_null isl_basic_map *isl_basic_map_free(
1991 __isl_take isl_basic_map *bmap);
1992 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1993 __isl_null isl_union_map *isl_union_map_free(
1994 __isl_take isl_union_map *umap);
1996 Other sets and relations can be constructed by starting
1997 from a universe set or relation, adding equality and/or
1998 inequality constraints and then projecting out the
1999 existentially quantified variables, if any.
2000 Constraints can be constructed, manipulated and
2001 added to (or removed from) (basic) sets and relations
2002 using the following functions.
2004 #include <isl/constraint.h>
2005 __isl_give isl_constraint *isl_constraint_alloc_equality(
2006 __isl_take isl_local_space *ls);
2007 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2008 __isl_take isl_local_space *ls);
2009 __isl_give isl_constraint *isl_constraint_set_constant_si(
2010 __isl_take isl_constraint *constraint, int v);
2011 __isl_give isl_constraint *isl_constraint_set_constant_val(
2012 __isl_take isl_constraint *constraint,
2013 __isl_take isl_val *v);
2014 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2015 __isl_take isl_constraint *constraint,
2016 enum isl_dim_type type, int pos, int v);
2017 __isl_give isl_constraint *
2018 isl_constraint_set_coefficient_val(
2019 __isl_take isl_constraint *constraint,
2020 enum isl_dim_type type, int pos,
2021 __isl_take isl_val *v);
2022 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2023 __isl_take isl_basic_map *bmap,
2024 __isl_take isl_constraint *constraint);
2025 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2026 __isl_take isl_basic_set *bset,
2027 __isl_take isl_constraint *constraint);
2028 __isl_give isl_map *isl_map_add_constraint(
2029 __isl_take isl_map *map,
2030 __isl_take isl_constraint *constraint);
2031 __isl_give isl_set *isl_set_add_constraint(
2032 __isl_take isl_set *set,
2033 __isl_take isl_constraint *constraint);
2035 For example, to create a set containing the even integers
2036 between 10 and 42, you would use the following code.
2039 isl_local_space *ls;
2041 isl_basic_set *bset;
2043 space = isl_space_set_alloc(ctx, 0, 2);
2044 bset = isl_basic_set_universe(isl_space_copy(space));
2045 ls = isl_local_space_from_space(space);
2047 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2048 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2049 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2050 bset = isl_basic_set_add_constraint(bset, c);
2052 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2053 c = isl_constraint_set_constant_si(c, -10);
2054 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2055 bset = isl_basic_set_add_constraint(bset, c);
2057 c = isl_constraint_alloc_inequality(ls);
2058 c = isl_constraint_set_constant_si(c, 42);
2059 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2060 bset = isl_basic_set_add_constraint(bset, c);
2062 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2066 isl_basic_set *bset;
2067 bset = isl_basic_set_read_from_str(ctx,
2068 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2070 A basic set or relation can also be constructed from two matrices
2071 describing the equalities and the inequalities.
2073 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2074 __isl_take isl_space *space,
2075 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2076 enum isl_dim_type c1,
2077 enum isl_dim_type c2, enum isl_dim_type c3,
2078 enum isl_dim_type c4);
2079 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2080 __isl_take isl_space *space,
2081 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2082 enum isl_dim_type c1,
2083 enum isl_dim_type c2, enum isl_dim_type c3,
2084 enum isl_dim_type c4, enum isl_dim_type c5);
2086 The C<isl_dim_type> arguments indicate the order in which
2087 different kinds of variables appear in the input matrices
2088 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2089 C<isl_dim_set> and C<isl_dim_div> for sets and
2090 of C<isl_dim_cst>, C<isl_dim_param>,
2091 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2093 A (basic or union) set or relation can also be constructed from a
2094 (union) (piecewise) (multiple) affine expression
2095 or a list of affine expressions
2096 (See L</"Functions">), provided these affine expressions do not
2099 #include <isl/set.h>
2100 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2101 __isl_take isl_multi_aff *ma);
2102 __isl_give isl_set *isl_set_from_multi_aff(
2103 __isl_take isl_multi_aff *ma);
2105 #include <isl/map.h>
2106 __isl_give isl_basic_map *isl_basic_map_from_aff(
2107 __isl_take isl_aff *aff);
2108 __isl_give isl_map *isl_map_from_aff(
2109 __isl_take isl_aff *aff);
2110 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2111 __isl_take isl_space *domain_space,
2112 __isl_take isl_aff_list *list);
2113 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2114 __isl_take isl_multi_aff *maff)
2115 __isl_give isl_map *isl_map_from_multi_aff(
2116 __isl_take isl_multi_aff *maff)
2118 #include <isl/aff.h>
2119 __isl_give isl_set *isl_set_from_pw_aff(
2120 __isl_take isl_pw_aff *pwaff);
2121 __isl_give isl_map *isl_map_from_pw_aff(
2122 __isl_take isl_pw_aff *pwaff);
2123 __isl_give isl_set *isl_set_from_pw_multi_aff(
2124 __isl_take isl_pw_multi_aff *pma);
2125 __isl_give isl_map *isl_map_from_pw_multi_aff(
2126 __isl_take isl_pw_multi_aff *pma);
2127 __isl_give isl_set *isl_set_from_multi_pw_aff(
2128 __isl_take isl_multi_pw_aff *mpa);
2129 __isl_give isl_map *isl_map_from_multi_pw_aff(
2130 __isl_take isl_multi_pw_aff *mpa);
2131 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2132 __isl_take isl_union_pw_aff *upa);
2133 __isl_give isl_union_map *
2134 isl_union_map_from_union_pw_multi_aff(
2135 __isl_take isl_union_pw_multi_aff *upma);
2136 __isl_give isl_union_map *
2137 isl_union_map_from_multi_union_pw_aff(
2138 __isl_take isl_multi_union_pw_aff *mupa);
2140 The C<domain_space> argument describes the domain of the resulting
2141 basic relation. It is required because the C<list> may consist
2142 of zero affine expressions.
2143 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2144 is not allowed to be zero-dimensional. The domain of the result
2145 is the shared domain of the union piecewise affine elements.
2147 =head2 Inspecting Sets and Relations
2149 Usually, the user should not have to care about the actual constraints
2150 of the sets and maps, but should instead apply the abstract operations
2151 explained in the following sections.
2152 Occasionally, however, it may be required to inspect the individual
2153 coefficients of the constraints. This section explains how to do so.
2154 In these cases, it may also be useful to have C<isl> compute
2155 an explicit representation of the existentially quantified variables.
2157 __isl_give isl_set *isl_set_compute_divs(
2158 __isl_take isl_set *set);
2159 __isl_give isl_map *isl_map_compute_divs(
2160 __isl_take isl_map *map);
2161 __isl_give isl_union_set *isl_union_set_compute_divs(
2162 __isl_take isl_union_set *uset);
2163 __isl_give isl_union_map *isl_union_map_compute_divs(
2164 __isl_take isl_union_map *umap);
2166 This explicit representation defines the existentially quantified
2167 variables as integer divisions of the other variables, possibly
2168 including earlier existentially quantified variables.
2169 An explicitly represented existentially quantified variable therefore
2170 has a unique value when the values of the other variables are known.
2172 Alternatively, the existentially quantified variables can be removed
2173 using the following functions, which compute an overapproximation.
2175 #include <isl/set.h>
2176 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2177 __isl_take isl_basic_set *bset);
2178 __isl_give isl_set *isl_set_remove_divs(
2179 __isl_take isl_set *set);
2181 #include <isl/map.h>
2182 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2183 __isl_take isl_basic_map *bmap);
2184 __isl_give isl_map *isl_map_remove_divs(
2185 __isl_take isl_map *map);
2187 #include <isl/union_set.h>
2188 __isl_give isl_union_set *isl_union_set_remove_divs(
2189 __isl_take isl_union_set *bset);
2191 #include <isl/union_map.h>
2192 __isl_give isl_union_map *isl_union_map_remove_divs(
2193 __isl_take isl_union_map *bmap);
2195 It is also possible to only remove those divs that are defined
2196 in terms of a given range of dimensions or only those for which
2197 no explicit representation is known.
2199 __isl_give isl_basic_set *
2200 isl_basic_set_remove_divs_involving_dims(
2201 __isl_take isl_basic_set *bset,
2202 enum isl_dim_type type,
2203 unsigned first, unsigned n);
2204 __isl_give isl_basic_map *
2205 isl_basic_map_remove_divs_involving_dims(
2206 __isl_take isl_basic_map *bmap,
2207 enum isl_dim_type type,
2208 unsigned first, unsigned n);
2209 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2210 __isl_take isl_set *set, enum isl_dim_type type,
2211 unsigned first, unsigned n);
2212 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2213 __isl_take isl_map *map, enum isl_dim_type type,
2214 unsigned first, unsigned n);
2216 __isl_give isl_basic_set *
2217 isl_basic_set_remove_unknown_divs(
2218 __isl_take isl_basic_set *bset);
2219 __isl_give isl_set *isl_set_remove_unknown_divs(
2220 __isl_take isl_set *set);
2221 __isl_give isl_map *isl_map_remove_unknown_divs(
2222 __isl_take isl_map *map);
2224 To iterate over all the sets or maps in a union set or map, use
2226 #include <isl/union_set.h>
2227 isl_stat isl_union_set_foreach_set(
2228 __isl_keep isl_union_set *uset,
2229 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2232 #include <isl/union_map.h>
2233 isl_stat isl_union_map_foreach_map(
2234 __isl_keep isl_union_map *umap,
2235 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2237 isl_bool isl_union_map_every_map(
2238 __isl_keep isl_union_map *umap,
2239 isl_bool (*test)(__isl_keep isl_map *map,
2243 These functions call the callback function once for each
2244 (pair of) space(s) for which there are elements in the input.
2245 The argument to the callback contains all elements in the input
2246 with that (pair of) space(s).
2247 The C<isl_union_map_every_map> variant check whether each
2248 call to the callback returns true and stops checking as soon as one
2249 of these calls returns false.
2251 The number of sets or maps in a union set or map can be obtained
2254 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2255 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2257 To extract the set or map in a given space from a union, use
2259 __isl_give isl_set *isl_union_set_extract_set(
2260 __isl_keep isl_union_set *uset,
2261 __isl_take isl_space *space);
2262 __isl_give isl_map *isl_union_map_extract_map(
2263 __isl_keep isl_union_map *umap,
2264 __isl_take isl_space *space);
2266 To iterate over all the basic sets or maps in a set or map, use
2268 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2269 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2272 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2273 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2277 The callback function C<fn> should return C<isl_stat_ok> if successful and
2278 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2279 occurs, the above functions will return C<isl_stat_error>.
2281 It should be noted that C<isl> does not guarantee that
2282 the basic sets or maps passed to C<fn> are disjoint.
2283 If this is required, then the user should call one of
2284 the following functions first.
2286 __isl_give isl_set *isl_set_make_disjoint(
2287 __isl_take isl_set *set);
2288 __isl_give isl_map *isl_map_make_disjoint(
2289 __isl_take isl_map *map);
2291 The number of basic sets in a set can be obtained
2292 or the number of basic maps in a map can be obtained
2295 #include <isl/set.h>
2296 int isl_set_n_basic_set(__isl_keep isl_set *set);
2298 #include <isl/map.h>
2299 int isl_map_n_basic_map(__isl_keep isl_map *map);
2301 It is also possible to obtain a list of (basic) sets from a set
2302 or union set, a list of basic maps from a map and a list of maps from a union
2305 #include <isl/set.h>
2306 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2307 __isl_keep isl_set *set);
2309 #include <isl/union_set.h>
2310 __isl_give isl_basic_set_list *
2311 isl_union_set_get_basic_set_list(
2312 __isl_keep isl_union_set *uset);
2313 __isl_give isl_set_list *isl_union_set_get_set_list(
2314 __isl_keep isl_union_set *uset);
2316 #include <isl/map.h>
2317 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2318 __isl_keep isl_map *map);
2320 #include <isl/union_map.h>
2321 __isl_give isl_map_list *isl_union_map_get_map_list(
2322 __isl_keep isl_union_map *umap);
2324 The returned list can be manipulated using the functions in L<"Lists">.
2326 To iterate over the constraints of a basic set or map, use
2328 #include <isl/constraint.h>
2330 int isl_basic_set_n_constraint(
2331 __isl_keep isl_basic_set *bset);
2332 isl_stat isl_basic_set_foreach_constraint(
2333 __isl_keep isl_basic_set *bset,
2334 isl_stat (*fn)(__isl_take isl_constraint *c,
2337 int isl_basic_map_n_constraint(
2338 __isl_keep isl_basic_map *bmap);
2339 isl_stat isl_basic_map_foreach_constraint(
2340 __isl_keep isl_basic_map *bmap,
2341 isl_stat (*fn)(__isl_take isl_constraint *c,
2344 __isl_null isl_constraint *isl_constraint_free(
2345 __isl_take isl_constraint *c);
2347 Again, the callback function C<fn> should return C<isl_stat_ok>
2349 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2350 occurs, the above functions will return C<isl_stat_error>.
2351 The constraint C<c> represents either an equality or an inequality.
2352 Use the following function to find out whether a constraint
2353 represents an equality. If not, it represents an inequality.
2355 isl_bool isl_constraint_is_equality(
2356 __isl_keep isl_constraint *constraint);
2358 It is also possible to obtain a list of constraints from a basic
2361 #include <isl/constraint.h>
2362 __isl_give isl_constraint_list *
2363 isl_basic_map_get_constraint_list(
2364 __isl_keep isl_basic_map *bmap);
2365 __isl_give isl_constraint_list *
2366 isl_basic_set_get_constraint_list(
2367 __isl_keep isl_basic_set *bset);
2369 These functions require that all existentially quantified variables
2370 have an explicit representation.
2371 The returned list can be manipulated using the functions in L<"Lists">.
2373 The coefficients of the constraints can be inspected using
2374 the following functions.
2376 isl_bool isl_constraint_is_lower_bound(
2377 __isl_keep isl_constraint *constraint,
2378 enum isl_dim_type type, unsigned pos);
2379 isl_bool isl_constraint_is_upper_bound(
2380 __isl_keep isl_constraint *constraint,
2381 enum isl_dim_type type, unsigned pos);
2382 __isl_give isl_val *isl_constraint_get_constant_val(
2383 __isl_keep isl_constraint *constraint);
2384 __isl_give isl_val *isl_constraint_get_coefficient_val(
2385 __isl_keep isl_constraint *constraint,
2386 enum isl_dim_type type, int pos);
2388 The explicit representations of the existentially quantified
2389 variables can be inspected using the following function.
2390 Note that the user is only allowed to use this function
2391 if the inspected set or map is the result of a call
2392 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2393 The existentially quantified variable is equal to the floor
2394 of the returned affine expression. The affine expression
2395 itself can be inspected using the functions in
2398 __isl_give isl_aff *isl_constraint_get_div(
2399 __isl_keep isl_constraint *constraint, int pos);
2401 To obtain the constraints of a basic set or map in matrix
2402 form, use the following functions.
2404 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2405 __isl_keep isl_basic_set *bset,
2406 enum isl_dim_type c1, enum isl_dim_type c2,
2407 enum isl_dim_type c3, enum isl_dim_type c4);
2408 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2409 __isl_keep isl_basic_set *bset,
2410 enum isl_dim_type c1, enum isl_dim_type c2,
2411 enum isl_dim_type c3, enum isl_dim_type c4);
2412 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2413 __isl_keep isl_basic_map *bmap,
2414 enum isl_dim_type c1,
2415 enum isl_dim_type c2, enum isl_dim_type c3,
2416 enum isl_dim_type c4, enum isl_dim_type c5);
2417 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2418 __isl_keep isl_basic_map *bmap,
2419 enum isl_dim_type c1,
2420 enum isl_dim_type c2, enum isl_dim_type c3,
2421 enum isl_dim_type c4, enum isl_dim_type c5);
2423 The C<isl_dim_type> arguments dictate the order in which
2424 different kinds of variables appear in the resulting matrix.
2425 For set inputs, they should be a permutation of
2426 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2427 For map inputs, they should be a permutation of
2428 C<isl_dim_cst>, C<isl_dim_param>,
2429 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2433 Points are elements of a set. They can be used to construct
2434 simple sets (boxes) or they can be used to represent the
2435 individual elements of a set.
2436 The zero point (the origin) can be created using
2438 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2440 The coordinates of a point can be inspected, set and changed
2443 __isl_give isl_val *isl_point_get_coordinate_val(
2444 __isl_keep isl_point *pnt,
2445 enum isl_dim_type type, int pos);
2446 __isl_give isl_point *isl_point_set_coordinate_val(
2447 __isl_take isl_point *pnt,
2448 enum isl_dim_type type, int pos,
2449 __isl_take isl_val *v);
2451 __isl_give isl_point *isl_point_add_ui(
2452 __isl_take isl_point *pnt,
2453 enum isl_dim_type type, int pos, unsigned val);
2454 __isl_give isl_point *isl_point_sub_ui(
2455 __isl_take isl_point *pnt,
2456 enum isl_dim_type type, int pos, unsigned val);
2458 Points can be copied or freed using
2460 __isl_give isl_point *isl_point_copy(
2461 __isl_keep isl_point *pnt);
2462 __isl_null isl_point *isl_point_free(
2463 __isl_take isl_point *pnt);
2465 A singleton set can be created from a point using
2467 __isl_give isl_basic_set *isl_basic_set_from_point(
2468 __isl_take isl_point *pnt);
2469 __isl_give isl_set *isl_set_from_point(
2470 __isl_take isl_point *pnt);
2471 __isl_give isl_union_set *isl_union_set_from_point(
2472 __isl_take isl_point *pnt);
2474 and a box can be created from two opposite extremal points using
2476 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2477 __isl_take isl_point *pnt1,
2478 __isl_take isl_point *pnt2);
2479 __isl_give isl_set *isl_set_box_from_points(
2480 __isl_take isl_point *pnt1,
2481 __isl_take isl_point *pnt2);
2483 All elements of a B<bounded> (union) set can be enumerated using
2484 the following functions.
2486 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2487 isl_stat (*fn)(__isl_take isl_point *pnt,
2490 isl_stat isl_union_set_foreach_point(
2491 __isl_keep isl_union_set *uset,
2492 isl_stat (*fn)(__isl_take isl_point *pnt,
2496 The function C<fn> is called for each integer point in
2497 C<set> with as second argument the last argument of
2498 the C<isl_set_foreach_point> call. The function C<fn>
2499 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2500 In the latter case, C<isl_set_foreach_point> will stop
2501 enumerating and return C<isl_stat_error> as well.
2502 If the enumeration is performed successfully and to completion,
2503 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2505 To obtain a single point of a (basic or union) set, use
2507 __isl_give isl_point *isl_basic_set_sample_point(
2508 __isl_take isl_basic_set *bset);
2509 __isl_give isl_point *isl_set_sample_point(
2510 __isl_take isl_set *set);
2511 __isl_give isl_point *isl_union_set_sample_point(
2512 __isl_take isl_union_set *uset);
2514 If C<set> does not contain any (integer) points, then the
2515 resulting point will be ``void'', a property that can be
2518 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2522 Besides sets and relation, C<isl> also supports various types of functions.
2523 Each of these types is derived from the value type (see L</"Values">)
2524 or from one of two primitive function types
2525 through the application of zero or more type constructors.
2526 We first describe the primitive type and then we describe
2527 the types derived from these primitive types.
2529 =head3 Primitive Functions
2531 C<isl> support two primitive function types, quasi-affine
2532 expressions and quasipolynomials.
2533 A quasi-affine expression is defined either over a parameter
2534 space or over a set and is composed of integer constants,
2535 parameters and set variables, addition, subtraction and
2536 integer division by an integer constant.
2537 For example, the quasi-affine expression
2539 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2541 maps C<x> to C<2*floor((4 n + x)/9>.
2542 A quasipolynomial is a polynomial expression in quasi-affine
2543 expression. That is, it additionally allows for multiplication.
2544 Note, though, that it is not allowed to construct an integer
2545 division of an expression involving multiplications.
2546 Here is an example of a quasipolynomial that is not
2547 quasi-affine expression
2549 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2551 Note that the external representations of quasi-affine expressions
2552 and quasipolynomials are different. Quasi-affine expressions
2553 use a notation with square brackets just like binary relations,
2554 while quasipolynomials do not. This might change at some point.
2556 If a primitive function is defined over a parameter space,
2557 then the space of the function itself is that of a set.
2558 If it is defined over a set, then the space of the function
2559 is that of a relation. In both cases, the set space (or
2560 the output space) is single-dimensional, anonymous and unstructured.
2561 To create functions with multiple dimensions or with other kinds
2562 of set or output spaces, use multiple expressions
2563 (see L</"Multiple Expressions">).
2567 =item * Quasi-affine Expressions
2569 Besides the expressions described above, a quasi-affine
2570 expression can also be set to NaN. Such expressions
2571 typically represent a failure to represent a result
2572 as a quasi-affine expression.
2574 The zero quasi affine expression or the quasi affine expression
2575 that is equal to a given value, parameter or
2576 a specified dimension on a given domain can be created using
2578 #include <isl/aff.h>
2579 __isl_give isl_aff *isl_aff_zero_on_domain(
2580 __isl_take isl_local_space *ls);
2581 __isl_give isl_aff *isl_aff_val_on_domain(
2582 __isl_take isl_local_space *ls,
2583 __isl_take isl_val *val);
2584 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2585 __isl_take isl_space *space,
2586 __isl_take isl_id *id);
2587 __isl_give isl_aff *isl_aff_var_on_domain(
2588 __isl_take isl_local_space *ls,
2589 enum isl_dim_type type, unsigned pos);
2590 __isl_give isl_aff *isl_aff_nan_on_domain(
2591 __isl_take isl_local_space *ls);
2593 The space passed to C<isl_aff_param_on_domain_space_id>
2594 is required to have a parameter with the given identifier.
2596 Quasi affine expressions can be copied and freed using
2598 #include <isl/aff.h>
2599 __isl_give isl_aff *isl_aff_copy(
2600 __isl_keep isl_aff *aff);
2601 __isl_null isl_aff *isl_aff_free(
2602 __isl_take isl_aff *aff);
2604 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2605 using the following function. The constraint is required to have
2606 a non-zero coefficient for the specified dimension.
2608 #include <isl/constraint.h>
2609 __isl_give isl_aff *isl_constraint_get_bound(
2610 __isl_keep isl_constraint *constraint,
2611 enum isl_dim_type type, int pos);
2613 The entire affine expression of the constraint can also be extracted
2614 using the following function.
2616 #include <isl/constraint.h>
2617 __isl_give isl_aff *isl_constraint_get_aff(
2618 __isl_keep isl_constraint *constraint);
2620 Conversely, an equality constraint equating
2621 the affine expression to zero or an inequality constraint enforcing
2622 the affine expression to be non-negative, can be constructed using
2624 __isl_give isl_constraint *isl_equality_from_aff(
2625 __isl_take isl_aff *aff);
2626 __isl_give isl_constraint *isl_inequality_from_aff(
2627 __isl_take isl_aff *aff);
2629 The coefficients and the integer divisions of an affine expression
2630 can be inspected using the following functions.
2632 #include <isl/aff.h>
2633 __isl_give isl_val *isl_aff_get_constant_val(
2634 __isl_keep isl_aff *aff);
2635 __isl_give isl_val *isl_aff_get_coefficient_val(
2636 __isl_keep isl_aff *aff,
2637 enum isl_dim_type type, int pos);
2638 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2639 enum isl_dim_type type, int pos);
2640 __isl_give isl_val *isl_aff_get_denominator_val(
2641 __isl_keep isl_aff *aff);
2642 __isl_give isl_aff *isl_aff_get_div(
2643 __isl_keep isl_aff *aff, int pos);
2645 They can be modified using the following functions.
2647 #include <isl/aff.h>
2648 __isl_give isl_aff *isl_aff_set_constant_si(
2649 __isl_take isl_aff *aff, int v);
2650 __isl_give isl_aff *isl_aff_set_constant_val(
2651 __isl_take isl_aff *aff, __isl_take isl_val *v);
2652 __isl_give isl_aff *isl_aff_set_coefficient_si(
2653 __isl_take isl_aff *aff,
2654 enum isl_dim_type type, int pos, int v);
2655 __isl_give isl_aff *isl_aff_set_coefficient_val(
2656 __isl_take isl_aff *aff,
2657 enum isl_dim_type type, int pos,
2658 __isl_take isl_val *v);
2660 __isl_give isl_aff *isl_aff_add_constant_si(
2661 __isl_take isl_aff *aff, int v);
2662 __isl_give isl_aff *isl_aff_add_constant_val(
2663 __isl_take isl_aff *aff, __isl_take isl_val *v);
2664 __isl_give isl_aff *isl_aff_add_constant_num_si(
2665 __isl_take isl_aff *aff, int v);
2666 __isl_give isl_aff *isl_aff_add_coefficient_si(
2667 __isl_take isl_aff *aff,
2668 enum isl_dim_type type, int pos, int v);
2669 __isl_give isl_aff *isl_aff_add_coefficient_val(
2670 __isl_take isl_aff *aff,
2671 enum isl_dim_type type, int pos,
2672 __isl_take isl_val *v);
2674 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2675 set the I<numerator> of the constant or coefficient, while
2676 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2677 the constant or coefficient as a whole.
2678 The C<add_constant> and C<add_coefficient> functions add an integer
2679 or rational value to
2680 the possibly rational constant or coefficient.
2681 The C<add_constant_num> functions add an integer value to
2684 =item * Quasipolynomials
2686 Some simple quasipolynomials can be created using the following functions.
2688 #include <isl/polynomial.h>
2689 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2690 __isl_take isl_space *domain);
2691 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2692 __isl_take isl_space *domain);
2693 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2694 __isl_take isl_space *domain);
2695 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2696 __isl_take isl_space *domain);
2697 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2698 __isl_take isl_space *domain);
2699 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2700 __isl_take isl_space *domain,
2701 __isl_take isl_val *val);
2702 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2703 __isl_take isl_space *domain,
2704 enum isl_dim_type type, unsigned pos);
2705 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2706 __isl_take isl_aff *aff);
2708 Recall that the space in which a quasipolynomial lives is a map space
2709 with a one-dimensional range. The C<domain> argument in some of
2710 the functions above corresponds to the domain of this map space.
2712 Quasipolynomials can be copied and freed again using the following
2715 #include <isl/polynomial.h>
2716 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2717 __isl_keep isl_qpolynomial *qp);
2718 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2719 __isl_take isl_qpolynomial *qp);
2721 The constant term of a quasipolynomial can be extracted using
2723 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2724 __isl_keep isl_qpolynomial *qp);
2726 To iterate over all terms in a quasipolynomial,
2729 isl_stat isl_qpolynomial_foreach_term(
2730 __isl_keep isl_qpolynomial *qp,
2731 isl_stat (*fn)(__isl_take isl_term *term,
2732 void *user), void *user);
2734 The terms themselves can be inspected and freed using
2737 unsigned isl_term_dim(__isl_keep isl_term *term,
2738 enum isl_dim_type type);
2739 __isl_give isl_val *isl_term_get_coefficient_val(
2740 __isl_keep isl_term *term);
2741 int isl_term_get_exp(__isl_keep isl_term *term,
2742 enum isl_dim_type type, unsigned pos);
2743 __isl_give isl_aff *isl_term_get_div(
2744 __isl_keep isl_term *term, unsigned pos);
2745 void isl_term_free(__isl_take isl_term *term);
2747 Each term is a product of parameters, set variables and
2748 integer divisions. The function C<isl_term_get_exp>
2749 returns the exponent of a given dimensions in the given term.
2755 A reduction represents a maximum or a minimum of its
2757 The only reduction type defined by C<isl> is
2758 C<isl_qpolynomial_fold>.
2760 There are currently no functions to directly create such
2761 objects, but they do appear in the piecewise quasipolynomial
2762 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2764 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2766 Reductions can be copied and freed using
2767 the following functions.
2769 #include <isl/polynomial.h>
2770 __isl_give isl_qpolynomial_fold *
2771 isl_qpolynomial_fold_copy(
2772 __isl_keep isl_qpolynomial_fold *fold);
2773 void isl_qpolynomial_fold_free(
2774 __isl_take isl_qpolynomial_fold *fold);
2776 To iterate over all quasipolynomials in a reduction, use
2778 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2779 __isl_keep isl_qpolynomial_fold *fold,
2780 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2781 void *user), void *user);
2783 =head3 Multiple Expressions
2785 A multiple expression represents a sequence of zero or
2786 more base expressions, all defined on the same domain space.
2787 The domain space of the multiple expression is the same
2788 as that of the base expressions, but the range space
2789 can be any space. In case the base expressions have
2790 a set space, the corresponding multiple expression
2791 also has a set space.
2792 Objects of the value type do not have an associated space.
2793 The space of a multiple value is therefore always a set space.
2794 Similarly, the space of a multiple union piecewise
2795 affine expression is always a set space.
2796 If the base expressions are not total, then
2797 a corresponding zero-dimensional multiple expression may
2798 have an explicit domain that keeps track of the domain
2799 outside of any base expressions.
2801 The multiple expression types defined by C<isl>
2802 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2803 C<isl_multi_union_pw_aff>.
2805 A multiple expression with the value zero for
2806 each output (or set) dimension can be created
2807 using the following functions.
2809 #include <isl/val.h>
2810 __isl_give isl_multi_val *isl_multi_val_zero(
2811 __isl_take isl_space *space);
2813 #include <isl/aff.h>
2814 __isl_give isl_multi_aff *isl_multi_aff_zero(
2815 __isl_take isl_space *space);
2816 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2817 __isl_take isl_space *space);
2818 __isl_give isl_multi_union_pw_aff *
2819 isl_multi_union_pw_aff_zero(
2820 __isl_take isl_space *space);
2822 Since there is no canonical way of representing a zero
2823 value of type C<isl_union_pw_aff>, the space passed
2824 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2826 An identity function can be created using the following
2827 functions. The space needs to be that of a relation
2828 with the same number of input and output dimensions.
2830 #include <isl/aff.h>
2831 __isl_give isl_multi_aff *isl_multi_aff_identity(
2832 __isl_take isl_space *space);
2833 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2834 __isl_take isl_space *space);
2836 A function that performs a projection on a universe
2837 relation or set can be created using the following functions.
2838 See also the corresponding
2839 projection operations in L</"Unary Operations">.
2841 #include <isl/aff.h>
2842 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2843 __isl_take isl_space *space);
2844 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2845 __isl_take isl_space *space);
2846 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2847 __isl_take isl_space *space,
2848 enum isl_dim_type type,
2849 unsigned first, unsigned n);
2851 A multiple expression can be created from a single
2852 base expression using the following functions.
2853 The space of the created multiple expression is the same
2854 as that of the base expression, except for
2855 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2856 lives in a parameter space and the output lives
2857 in a single-dimensional set space.
2859 #include <isl/aff.h>
2860 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2861 __isl_take isl_aff *aff);
2862 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2863 __isl_take isl_pw_aff *pa);
2864 __isl_give isl_multi_union_pw_aff *
2865 isl_multi_union_pw_aff_from_union_pw_aff(
2866 __isl_take isl_union_pw_aff *upa);
2868 A multiple expression can be created from a list
2869 of base expression in a specified space.
2870 The domain of this space needs to be the same
2871 as the domains of the base expressions in the list.
2872 If the base expressions have a set space (or no associated space),
2873 then this space also needs to be a set space.
2875 #include <isl/val.h>
2876 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2877 __isl_take isl_space *space,
2878 __isl_take isl_val_list *list);
2880 #include <isl/aff.h>
2881 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2882 __isl_take isl_space *space,
2883 __isl_take isl_aff_list *list);
2884 __isl_give isl_multi_pw_aff *
2885 isl_multi_pw_aff_from_pw_aff_list(
2886 __isl_take isl_space *space,
2887 __isl_take isl_pw_aff_list *list);
2888 __isl_give isl_multi_union_pw_aff *
2889 isl_multi_union_pw_aff_from_union_pw_aff_list(
2890 __isl_take isl_space *space,
2891 __isl_take isl_union_pw_aff_list *list);
2893 As a convenience, a multiple piecewise expression can
2894 also be created from a multiple expression.
2895 Each piecewise expression in the result has a single
2898 #include <isl/aff.h>
2899 __isl_give isl_multi_pw_aff *
2900 isl_multi_pw_aff_from_multi_aff(
2901 __isl_take isl_multi_aff *ma);
2903 Similarly, a multiple union expression can be
2904 created from a multiple expression.
2906 #include <isl/aff.h>
2907 __isl_give isl_multi_union_pw_aff *
2908 isl_multi_union_pw_aff_from_multi_aff(
2909 __isl_take isl_multi_aff *ma);
2910 __isl_give isl_multi_union_pw_aff *
2911 isl_multi_union_pw_aff_from_multi_pw_aff(
2912 __isl_take isl_multi_pw_aff *mpa);
2914 A multiple quasi-affine expression can be created from
2915 a multiple value with a given domain space using the following
2918 #include <isl/aff.h>
2919 __isl_give isl_multi_aff *
2920 isl_multi_aff_multi_val_on_space(
2921 __isl_take isl_space *space,
2922 __isl_take isl_multi_val *mv);
2925 a multiple union piecewise affine expression can be created from
2926 a multiple value with a given domain or
2927 a (piecewise) multiple affine expression with a given domain
2928 using the following functions.
2930 #include <isl/aff.h>
2931 __isl_give isl_multi_union_pw_aff *
2932 isl_multi_union_pw_aff_multi_val_on_domain(
2933 __isl_take isl_union_set *domain,
2934 __isl_take isl_multi_val *mv);
2935 __isl_give isl_multi_union_pw_aff *
2936 isl_multi_union_pw_aff_multi_aff_on_domain(
2937 __isl_take isl_union_set *domain,
2938 __isl_take isl_multi_aff *ma);
2939 __isl_give isl_multi_union_pw_aff *
2940 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2941 __isl_take isl_union_set *domain,
2942 __isl_take isl_pw_multi_aff *pma);
2944 Multiple expressions can be copied and freed using
2945 the following functions.
2947 #include <isl/val.h>
2948 __isl_give isl_multi_val *isl_multi_val_copy(
2949 __isl_keep isl_multi_val *mv);
2950 __isl_null isl_multi_val *isl_multi_val_free(
2951 __isl_take isl_multi_val *mv);
2953 #include <isl/aff.h>
2954 __isl_give isl_multi_aff *isl_multi_aff_copy(
2955 __isl_keep isl_multi_aff *maff);
2956 __isl_null isl_multi_aff *isl_multi_aff_free(
2957 __isl_take isl_multi_aff *maff);
2958 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2959 __isl_keep isl_multi_pw_aff *mpa);
2960 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2961 __isl_take isl_multi_pw_aff *mpa);
2962 __isl_give isl_multi_union_pw_aff *
2963 isl_multi_union_pw_aff_copy(
2964 __isl_keep isl_multi_union_pw_aff *mupa);
2965 __isl_null isl_multi_union_pw_aff *
2966 isl_multi_union_pw_aff_free(
2967 __isl_take isl_multi_union_pw_aff *mupa);
2969 The base expression at a given position of a multiple
2970 expression can be extracted using the following functions.
2972 #include <isl/val.h>
2973 __isl_give isl_val *isl_multi_val_get_val(
2974 __isl_keep isl_multi_val *mv, int pos);
2976 #include <isl/aff.h>
2977 __isl_give isl_aff *isl_multi_aff_get_aff(
2978 __isl_keep isl_multi_aff *multi, int pos);
2979 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2980 __isl_keep isl_multi_pw_aff *mpa, int pos);
2981 __isl_give isl_union_pw_aff *
2982 isl_multi_union_pw_aff_get_union_pw_aff(
2983 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2985 It can be replaced using the following functions.
2987 #include <isl/val.h>
2988 __isl_give isl_multi_val *isl_multi_val_set_val(
2989 __isl_take isl_multi_val *mv, int pos,
2990 __isl_take isl_val *val);
2992 #include <isl/aff.h>
2993 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2994 __isl_take isl_multi_aff *multi, int pos,
2995 __isl_take isl_aff *aff);
2996 __isl_give isl_multi_union_pw_aff *
2997 isl_multi_union_pw_aff_set_union_pw_aff(
2998 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2999 __isl_take isl_union_pw_aff *upa);
3001 As a convenience, a sequence of base expressions that have
3002 their domains in a given space can be extracted from a sequence
3003 of union expressions using the following function.
3005 #include <isl/aff.h>
3006 __isl_give isl_multi_pw_aff *
3007 isl_multi_union_pw_aff_extract_multi_pw_aff(
3008 __isl_keep isl_multi_union_pw_aff *mupa,
3009 __isl_take isl_space *space);
3011 Note that there is a difference between C<isl_multi_union_pw_aff>
3012 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3013 of unions of piecewise expressions, while the second is a union
3014 of piecewise sequences. In particular, multiple affine expressions
3015 in an C<isl_union_pw_multi_aff> may live in different spaces,
3016 while there is only a single multiple expression in
3017 an C<isl_multi_union_pw_aff>, which can therefore only live
3018 in a single space. This means that not every
3019 C<isl_union_pw_multi_aff> can be converted to
3020 an C<isl_multi_union_pw_aff>. Conversely, the elements
3021 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3022 while each multiple expression inside an C<isl_union_pw_multi_aff>
3023 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3024 of dimension greater than one may therefore not be exact.
3025 The following functions can
3026 be used to perform these conversions when they are possible.
3028 #include <isl/aff.h>
3029 __isl_give isl_multi_union_pw_aff *
3030 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3031 __isl_take isl_union_pw_multi_aff *upma);
3032 __isl_give isl_union_pw_multi_aff *
3033 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3034 __isl_take isl_multi_union_pw_aff *mupa);
3036 =head3 Piecewise Expressions
3038 A piecewise expression is an expression that is described
3039 using zero or more base expression defined over the same
3040 number of cells in the domain space of the base expressions.
3041 All base expressions are defined over the same
3042 domain space and the cells are disjoint.
3043 The space of a piecewise expression is the same as
3044 that of the base expressions.
3045 If the union of the cells is a strict subset of the domain
3046 space, then the value of the piecewise expression outside
3047 this union is different for types derived from quasi-affine
3048 expressions and those derived from quasipolynomials.
3049 Piecewise expressions derived from quasi-affine expressions
3050 are considered to be undefined outside the union of their cells.
3051 Piecewise expressions derived from quasipolynomials
3052 are considered to be zero outside the union of their cells.
3054 Piecewise quasipolynomials are mainly used by the C<barvinok>
3055 library for representing the number of elements in a parametric set or map.
3056 For example, the piecewise quasipolynomial
3058 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3060 represents the number of points in the map
3062 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3064 The piecewise expression types defined by C<isl>
3065 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3066 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3068 A piecewise expression with no cells can be created using
3069 the following functions.
3071 #include <isl/aff.h>
3072 __isl_give isl_pw_aff *isl_pw_aff_empty(
3073 __isl_take isl_space *space);
3074 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3075 __isl_take isl_space *space);
3077 A piecewise expression with a single universe cell can be
3078 created using the following functions.
3080 #include <isl/aff.h>
3081 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3082 __isl_take isl_aff *aff);
3083 __isl_give isl_pw_multi_aff *
3084 isl_pw_multi_aff_from_multi_aff(
3085 __isl_take isl_multi_aff *ma);
3087 #include <isl/polynomial.h>
3088 __isl_give isl_pw_qpolynomial *
3089 isl_pw_qpolynomial_from_qpolynomial(
3090 __isl_take isl_qpolynomial *qp);
3092 A piecewise expression with a single specified cell can be
3093 created using the following functions.
3095 #include <isl/aff.h>
3096 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3097 __isl_take isl_set *set, __isl_take isl_aff *aff);
3098 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3099 __isl_take isl_set *set,
3100 __isl_take isl_multi_aff *maff);
3102 #include <isl/polynomial.h>
3103 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3104 __isl_take isl_set *set,
3105 __isl_take isl_qpolynomial *qp);
3107 The following convenience functions first create a base expression and
3108 then create a piecewise expression over a universe domain.
3110 #include <isl/aff.h>
3111 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3112 __isl_take isl_local_space *ls);
3113 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3114 __isl_take isl_local_space *ls,
3115 enum isl_dim_type type, unsigned pos);
3116 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3117 __isl_take isl_local_space *ls);
3118 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3119 __isl_take isl_space *space);
3120 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3121 __isl_take isl_space *space);
3122 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3123 __isl_take isl_space *space);
3124 __isl_give isl_pw_multi_aff *
3125 isl_pw_multi_aff_project_out_map(
3126 __isl_take isl_space *space,
3127 enum isl_dim_type type,
3128 unsigned first, unsigned n);
3130 #include <isl/polynomial.h>
3131 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3132 __isl_take isl_space *space);
3134 The following convenience functions first create a base expression and
3135 then create a piecewise expression over a given domain.
3137 #include <isl/aff.h>
3138 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3139 __isl_take isl_set *domain,
3140 __isl_take isl_val *v);
3141 __isl_give isl_pw_multi_aff *
3142 isl_pw_multi_aff_multi_val_on_domain(
3143 __isl_take isl_set *domain,
3144 __isl_take isl_multi_val *mv);
3146 As a convenience, a piecewise multiple expression can
3147 also be created from a piecewise expression.
3148 Each multiple expression in the result is derived
3149 from the corresponding base expression.
3151 #include <isl/aff.h>
3152 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3153 __isl_take isl_pw_aff *pa);
3155 Similarly, a piecewise quasipolynomial can be
3156 created from a piecewise quasi-affine expression using
3157 the following function.
3159 #include <isl/polynomial.h>
3160 __isl_give isl_pw_qpolynomial *
3161 isl_pw_qpolynomial_from_pw_aff(
3162 __isl_take isl_pw_aff *pwaff);
3164 Piecewise expressions can be copied and freed using the following functions.
3166 #include <isl/aff.h>
3167 __isl_give isl_pw_aff *isl_pw_aff_copy(
3168 __isl_keep isl_pw_aff *pwaff);
3169 __isl_null isl_pw_aff *isl_pw_aff_free(
3170 __isl_take isl_pw_aff *pwaff);
3171 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3172 __isl_keep isl_pw_multi_aff *pma);
3173 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3174 __isl_take isl_pw_multi_aff *pma);
3176 #include <isl/polynomial.h>
3177 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3178 __isl_keep isl_pw_qpolynomial *pwqp);
3179 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3180 __isl_take isl_pw_qpolynomial *pwqp);
3181 __isl_give isl_pw_qpolynomial_fold *
3182 isl_pw_qpolynomial_fold_copy(
3183 __isl_keep isl_pw_qpolynomial_fold *pwf);
3184 __isl_null isl_pw_qpolynomial_fold *
3185 isl_pw_qpolynomial_fold_free(
3186 __isl_take isl_pw_qpolynomial_fold *pwf);
3188 To iterate over the different cells of a piecewise expression,
3189 use the following functions.
3191 #include <isl/aff.h>
3192 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3193 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3194 isl_stat isl_pw_aff_foreach_piece(
3195 __isl_keep isl_pw_aff *pwaff,
3196 isl_stat (*fn)(__isl_take isl_set *set,
3197 __isl_take isl_aff *aff,
3198 void *user), void *user);
3199 int isl_pw_multi_aff_n_piece(
3200 __isl_keep isl_pw_multi_aff *pma);
3201 isl_stat isl_pw_multi_aff_foreach_piece(
3202 __isl_keep isl_pw_multi_aff *pma,
3203 isl_stat (*fn)(__isl_take isl_set *set,
3204 __isl_take isl_multi_aff *maff,
3205 void *user), void *user);
3207 #include <isl/polynomial.h>
3208 int isl_pw_qpolynomial_n_piece(
3209 __isl_keep isl_pw_qpolynomial *pwqp);
3210 isl_stat isl_pw_qpolynomial_foreach_piece(
3211 __isl_keep isl_pw_qpolynomial *pwqp,
3212 isl_stat (*fn)(__isl_take isl_set *set,
3213 __isl_take isl_qpolynomial *qp,
3214 void *user), void *user);
3215 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3216 __isl_keep isl_pw_qpolynomial *pwqp,
3217 isl_stat (*fn)(__isl_take isl_set *set,
3218 __isl_take isl_qpolynomial *qp,
3219 void *user), void *user);
3220 int isl_pw_qpolynomial_fold_n_piece(
3221 __isl_keep isl_pw_qpolynomial_fold *pwf);
3222 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3223 __isl_keep isl_pw_qpolynomial_fold *pwf,
3224 isl_stat (*fn)(__isl_take isl_set *set,
3225 __isl_take isl_qpolynomial_fold *fold,
3226 void *user), void *user);
3227 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3228 __isl_keep isl_pw_qpolynomial_fold *pwf,
3229 isl_stat (*fn)(__isl_take isl_set *set,
3230 __isl_take isl_qpolynomial_fold *fold,
3231 void *user), void *user);
3233 As usual, the function C<fn> should return C<isl_stat_ok> on success
3234 and C<isl_stat_error> on failure. The difference between
3235 C<isl_pw_qpolynomial_foreach_piece> and
3236 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3237 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3238 compute unique representations for all existentially quantified
3239 variables and then turn these existentially quantified variables
3240 into extra set variables, adapting the associated quasipolynomial
3241 accordingly. This means that the C<set> passed to C<fn>
3242 will not have any existentially quantified variables, but that
3243 the dimensions of the sets may be different for different
3244 invocations of C<fn>.
3245 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3246 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3248 A piecewise expression consisting of the expressions at a given
3249 position of a piecewise multiple expression can be extracted
3250 using the following function.
3252 #include <isl/aff.h>
3253 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3254 __isl_keep isl_pw_multi_aff *pma, int pos);
3256 These expressions can be replaced using the following function.
3258 #include <isl/aff.h>
3259 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3260 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3261 __isl_take isl_pw_aff *pa);
3263 Note that there is a difference between C<isl_multi_pw_aff> and
3264 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3265 affine expressions, while the second is a piecewise sequence
3266 of affine expressions. In particular, each of the piecewise
3267 affine expressions in an C<isl_multi_pw_aff> may have a different
3268 domain, while all multiple expressions associated to a cell
3269 in an C<isl_pw_multi_aff> have the same domain.
3270 It is possible to convert between the two, but when converting
3271 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3272 of the result is the intersection of the domains of the input.
3273 The reverse conversion is exact.
3275 #include <isl/aff.h>
3276 __isl_give isl_pw_multi_aff *
3277 isl_pw_multi_aff_from_multi_pw_aff(
3278 __isl_take isl_multi_pw_aff *mpa);
3279 __isl_give isl_multi_pw_aff *
3280 isl_multi_pw_aff_from_pw_multi_aff(
3281 __isl_take isl_pw_multi_aff *pma);
3283 =head3 Union Expressions
3285 A union expression collects base expressions defined
3286 over different domains. The space of a union expression
3287 is that of the shared parameter space.
3289 The union expression types defined by C<isl>
3290 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3291 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3293 C<isl_union_pw_aff>,
3294 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3295 there can be at most one base expression for a given domain space.
3297 C<isl_union_pw_multi_aff>,
3298 there can be multiple such expressions for a given domain space,
3299 but the domains of these expressions need to be disjoint.
3301 An empty union expression can be created using the following functions.
3303 #include <isl/aff.h>
3304 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3305 __isl_take isl_space *space);
3306 __isl_give isl_union_pw_multi_aff *
3307 isl_union_pw_multi_aff_empty(
3308 __isl_take isl_space *space);
3310 #include <isl/polynomial.h>
3311 __isl_give isl_union_pw_qpolynomial *
3312 isl_union_pw_qpolynomial_zero(
3313 __isl_take isl_space *space);
3315 A union expression containing a single base expression
3316 can be created using the following functions.
3318 #include <isl/aff.h>
3319 __isl_give isl_union_pw_aff *
3320 isl_union_pw_aff_from_pw_aff(
3321 __isl_take isl_pw_aff *pa);
3322 __isl_give isl_union_pw_multi_aff *
3323 isl_union_pw_multi_aff_from_aff(
3324 __isl_take isl_aff *aff);
3325 __isl_give isl_union_pw_multi_aff *
3326 isl_union_pw_multi_aff_from_pw_multi_aff(
3327 __isl_take isl_pw_multi_aff *pma);
3329 #include <isl/polynomial.h>
3330 __isl_give isl_union_pw_qpolynomial *
3331 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3332 __isl_take isl_pw_qpolynomial *pwqp);
3334 The following functions create a base expression on each
3335 of the sets in the union set and collect the results.
3337 #include <isl/aff.h>
3338 __isl_give isl_union_pw_multi_aff *
3339 isl_union_pw_multi_aff_from_union_pw_aff(
3340 __isl_take isl_union_pw_aff *upa);
3341 __isl_give isl_union_pw_aff *
3342 isl_union_pw_multi_aff_get_union_pw_aff(
3343 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3344 __isl_give isl_union_pw_aff *
3345 isl_union_pw_aff_val_on_domain(
3346 __isl_take isl_union_set *domain,
3347 __isl_take isl_val *v);
3348 __isl_give isl_union_pw_multi_aff *
3349 isl_union_pw_multi_aff_multi_val_on_domain(
3350 __isl_take isl_union_set *domain,
3351 __isl_take isl_multi_val *mv);
3352 __isl_give isl_union_pw_aff *
3353 isl_union_pw_aff_param_on_domain_id(
3354 __isl_take isl_union_set *domain,
3355 __isl_take isl_id *id);
3357 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3358 is the identifier of a parameter that may or may not already
3359 be present in C<domain>.
3361 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3363 expression on a given domain can be created using the following
3366 #include <isl/aff.h>
3367 __isl_give isl_union_pw_aff *
3368 isl_union_pw_aff_aff_on_domain(
3369 __isl_take isl_union_set *domain,
3370 __isl_take isl_aff *aff);
3371 __isl_give isl_union_pw_aff *
3372 isl_union_pw_aff_pw_aff_on_domain(
3373 __isl_take isl_union_set *domain,
3374 __isl_take isl_pw_aff *pa);
3376 A base expression can be added to a union expression using
3377 the following functions.
3379 #include <isl/aff.h>
3380 __isl_give isl_union_pw_aff *
3381 isl_union_pw_aff_add_pw_aff(
3382 __isl_take isl_union_pw_aff *upa,
3383 __isl_take isl_pw_aff *pa);
3384 __isl_give isl_union_pw_multi_aff *
3385 isl_union_pw_multi_aff_add_pw_multi_aff(
3386 __isl_take isl_union_pw_multi_aff *upma,
3387 __isl_take isl_pw_multi_aff *pma);
3389 #include <isl/polynomial.h>
3390 __isl_give isl_union_pw_qpolynomial *
3391 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3392 __isl_take isl_union_pw_qpolynomial *upwqp,
3393 __isl_take isl_pw_qpolynomial *pwqp);
3395 Union expressions can be copied and freed using
3396 the following functions.
3398 #include <isl/aff.h>
3399 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3400 __isl_keep isl_union_pw_aff *upa);
3401 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3402 __isl_take isl_union_pw_aff *upa);
3403 __isl_give isl_union_pw_multi_aff *
3404 isl_union_pw_multi_aff_copy(
3405 __isl_keep isl_union_pw_multi_aff *upma);
3406 __isl_null isl_union_pw_multi_aff *
3407 isl_union_pw_multi_aff_free(
3408 __isl_take isl_union_pw_multi_aff *upma);
3410 #include <isl/polynomial.h>
3411 __isl_give isl_union_pw_qpolynomial *
3412 isl_union_pw_qpolynomial_copy(
3413 __isl_keep isl_union_pw_qpolynomial *upwqp);
3414 __isl_null isl_union_pw_qpolynomial *
3415 isl_union_pw_qpolynomial_free(
3416 __isl_take isl_union_pw_qpolynomial *upwqp);
3417 __isl_give isl_union_pw_qpolynomial_fold *
3418 isl_union_pw_qpolynomial_fold_copy(
3419 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3420 __isl_null isl_union_pw_qpolynomial_fold *
3421 isl_union_pw_qpolynomial_fold_free(
3422 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3424 To iterate over the base expressions in a union expression,
3425 use the following functions.
3427 #include <isl/aff.h>
3428 int isl_union_pw_aff_n_pw_aff(
3429 __isl_keep isl_union_pw_aff *upa);
3430 isl_stat isl_union_pw_aff_foreach_pw_aff(
3431 __isl_keep isl_union_pw_aff *upa,
3432 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3433 void *user), void *user);
3434 int isl_union_pw_multi_aff_n_pw_multi_aff(
3435 __isl_keep isl_union_pw_multi_aff *upma);
3436 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3437 __isl_keep isl_union_pw_multi_aff *upma,
3438 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3439 void *user), void *user);
3441 #include <isl/polynomial.h>
3442 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3443 __isl_keep isl_union_pw_qpolynomial *upwqp);
3444 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3445 __isl_keep isl_union_pw_qpolynomial *upwqp,
3446 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3447 void *user), void *user);
3448 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3449 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3450 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3451 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3452 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3453 void *user), void *user);
3455 To extract the base expression in a given space from a union, use
3456 the following functions.
3458 #include <isl/aff.h>
3459 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3460 __isl_keep isl_union_pw_aff *upa,
3461 __isl_take isl_space *space);
3462 __isl_give isl_pw_multi_aff *
3463 isl_union_pw_multi_aff_extract_pw_multi_aff(
3464 __isl_keep isl_union_pw_multi_aff *upma,
3465 __isl_take isl_space *space);
3467 #include <isl/polynomial.h>
3468 __isl_give isl_pw_qpolynomial *
3469 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3470 __isl_keep isl_union_pw_qpolynomial *upwqp,
3471 __isl_take isl_space *space);
3473 It is also possible to obtain a list of the base expressions using
3474 the following functions.
3476 #include <isl/aff.h>
3477 __isl_give isl_pw_aff_list *
3478 isl_union_pw_aff_get_pw_aff_list(
3479 __isl_keep isl_union_pw_aff *upa);
3480 __isl_give isl_pw_multi_aff_list *
3481 isl_union_pw_multi_aff_get_pw_multi_aff_list(
3482 __isl_keep isl_union_pw_multi_aff *upma);
3484 #include <isl/polynomial.h>
3485 __isl_give isl_pw_qpolynomial_list *
3486 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
3487 __isl_keep isl_union_pw_qpolynomial *upwqp);
3488 __isl_give isl_pw_qpolynomial_fold_list *
3489 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
3490 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3492 The returned list can be manipulated using the functions in L<"Lists">.
3494 =head2 Input and Output
3496 For set and relation,
3497 C<isl> supports its own input/output format, which is similar
3498 to the C<Omega> format, but also supports the C<PolyLib> format
3500 For other object types, typically only an C<isl> format is supported.
3502 =head3 C<isl> format
3504 The C<isl> format is similar to that of C<Omega>, but has a different
3505 syntax for describing the parameters and allows for the definition
3506 of an existentially quantified variable as the integer division
3507 of an affine expression.
3508 For example, the set of integers C<i> between C<0> and C<n>
3509 such that C<i % 10 <= 6> can be described as
3511 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3514 A set or relation can have several disjuncts, separated
3515 by the keyword C<or>. Each disjunct is either a conjunction
3516 of constraints or a projection (C<exists>) of a conjunction
3517 of constraints. The constraints are separated by the keyword
3520 =head3 C<PolyLib> format
3522 If the represented set is a union, then the first line
3523 contains a single number representing the number of disjuncts.
3524 Otherwise, a line containing the number C<1> is optional.
3526 Each disjunct is represented by a matrix of constraints.
3527 The first line contains two numbers representing
3528 the number of rows and columns,
3529 where the number of rows is equal to the number of constraints
3530 and the number of columns is equal to two plus the number of variables.
3531 The following lines contain the actual rows of the constraint matrix.
3532 In each row, the first column indicates whether the constraint
3533 is an equality (C<0>) or inequality (C<1>). The final column
3534 corresponds to the constant term.
3536 If the set is parametric, then the coefficients of the parameters
3537 appear in the last columns before the constant column.
3538 The coefficients of any existentially quantified variables appear
3539 between those of the set variables and those of the parameters.
3541 =head3 Extended C<PolyLib> format
3543 The extended C<PolyLib> format is nearly identical to the
3544 C<PolyLib> format. The only difference is that the line
3545 containing the number of rows and columns of a constraint matrix
3546 also contains four additional numbers:
3547 the number of output dimensions, the number of input dimensions,
3548 the number of local dimensions (i.e., the number of existentially
3549 quantified variables) and the number of parameters.
3550 For sets, the number of ``output'' dimensions is equal
3551 to the number of set dimensions, while the number of ``input''
3556 Objects can be read from input using the following functions.
3558 #include <isl/val.h>
3559 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3561 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3562 isl_ctx *ctx, const char *str);
3564 #include <isl/set.h>
3565 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3566 isl_ctx *ctx, FILE *input);
3567 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3568 isl_ctx *ctx, const char *str);
3569 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3571 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3574 #include <isl/map.h>
3575 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3576 isl_ctx *ctx, FILE *input);
3577 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3578 isl_ctx *ctx, const char *str);
3579 __isl_give isl_map *isl_map_read_from_file(
3580 isl_ctx *ctx, FILE *input);
3581 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3584 #include <isl/union_set.h>
3585 __isl_give isl_union_set *isl_union_set_read_from_file(
3586 isl_ctx *ctx, FILE *input);
3587 __isl_give isl_union_set *isl_union_set_read_from_str(
3588 isl_ctx *ctx, const char *str);
3590 #include <isl/union_map.h>
3591 __isl_give isl_union_map *isl_union_map_read_from_file(
3592 isl_ctx *ctx, FILE *input);
3593 __isl_give isl_union_map *isl_union_map_read_from_str(
3594 isl_ctx *ctx, const char *str);
3596 #include <isl/aff.h>
3597 __isl_give isl_aff *isl_aff_read_from_str(
3598 isl_ctx *ctx, const char *str);
3599 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3600 isl_ctx *ctx, const char *str);
3601 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3602 isl_ctx *ctx, const char *str);
3603 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3604 isl_ctx *ctx, const char *str);
3605 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3606 isl_ctx *ctx, const char *str);
3607 __isl_give isl_union_pw_aff *
3608 isl_union_pw_aff_read_from_str(
3609 isl_ctx *ctx, const char *str);
3610 __isl_give isl_union_pw_multi_aff *
3611 isl_union_pw_multi_aff_read_from_str(
3612 isl_ctx *ctx, const char *str);
3613 __isl_give isl_multi_union_pw_aff *
3614 isl_multi_union_pw_aff_read_from_str(
3615 isl_ctx *ctx, const char *str);
3617 #include <isl/polynomial.h>
3618 __isl_give isl_union_pw_qpolynomial *
3619 isl_union_pw_qpolynomial_read_from_str(
3620 isl_ctx *ctx, const char *str);
3622 For sets and relations,
3623 the input format is autodetected and may be either the C<PolyLib> format
3624 or the C<isl> format.
3628 Before anything can be printed, an C<isl_printer> needs to
3631 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3633 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3634 __isl_null isl_printer *isl_printer_free(
3635 __isl_take isl_printer *printer);
3637 C<isl_printer_to_file> prints to the given file, while
3638 C<isl_printer_to_str> prints to a string that can be extracted
3639 using the following function.
3641 #include <isl/printer.h>
3642 __isl_give char *isl_printer_get_str(
3643 __isl_keep isl_printer *printer);
3645 The printer can be inspected using the following functions.
3647 FILE *isl_printer_get_file(
3648 __isl_keep isl_printer *printer);
3649 int isl_printer_get_output_format(
3650 __isl_keep isl_printer *p);
3651 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3653 The behavior of the printer can be modified in various ways
3655 __isl_give isl_printer *isl_printer_set_output_format(
3656 __isl_take isl_printer *p, int output_format);
3657 __isl_give isl_printer *isl_printer_set_indent(
3658 __isl_take isl_printer *p, int indent);
3659 __isl_give isl_printer *isl_printer_set_indent_prefix(
3660 __isl_take isl_printer *p, const char *prefix);
3661 __isl_give isl_printer *isl_printer_indent(
3662 __isl_take isl_printer *p, int indent);
3663 __isl_give isl_printer *isl_printer_set_prefix(
3664 __isl_take isl_printer *p, const char *prefix);
3665 __isl_give isl_printer *isl_printer_set_suffix(
3666 __isl_take isl_printer *p, const char *suffix);
3667 __isl_give isl_printer *isl_printer_set_yaml_style(
3668 __isl_take isl_printer *p, int yaml_style);
3670 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3671 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3672 and defaults to C<ISL_FORMAT_ISL>.
3673 Each line in the output is prefixed by C<indent_prefix>,
3674 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3675 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3676 In the C<PolyLib> format output,
3677 the coefficients of the existentially quantified variables
3678 appear between those of the set variables and those
3680 The function C<isl_printer_indent> increases the indentation
3681 by the specified amount (which may be negative).
3682 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3683 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3686 To actually print something, use
3688 #include <isl/printer.h>
3689 __isl_give isl_printer *isl_printer_print_double(
3690 __isl_take isl_printer *p, double d);
3692 #include <isl/val.h>
3693 __isl_give isl_printer *isl_printer_print_val(
3694 __isl_take isl_printer *p, __isl_keep isl_val *v);
3696 #include <isl/set.h>
3697 __isl_give isl_printer *isl_printer_print_basic_set(
3698 __isl_take isl_printer *printer,
3699 __isl_keep isl_basic_set *bset);
3700 __isl_give isl_printer *isl_printer_print_set(
3701 __isl_take isl_printer *printer,
3702 __isl_keep isl_set *set);
3704 #include <isl/map.h>
3705 __isl_give isl_printer *isl_printer_print_basic_map(
3706 __isl_take isl_printer *printer,
3707 __isl_keep isl_basic_map *bmap);
3708 __isl_give isl_printer *isl_printer_print_map(
3709 __isl_take isl_printer *printer,
3710 __isl_keep isl_map *map);
3712 #include <isl/union_set.h>
3713 __isl_give isl_printer *isl_printer_print_union_set(
3714 __isl_take isl_printer *p,
3715 __isl_keep isl_union_set *uset);
3717 #include <isl/union_map.h>
3718 __isl_give isl_printer *isl_printer_print_union_map(
3719 __isl_take isl_printer *p,
3720 __isl_keep isl_union_map *umap);
3722 #include <isl/val.h>
3723 __isl_give isl_printer *isl_printer_print_multi_val(
3724 __isl_take isl_printer *p,
3725 __isl_keep isl_multi_val *mv);
3727 #include <isl/aff.h>
3728 __isl_give isl_printer *isl_printer_print_aff(
3729 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3730 __isl_give isl_printer *isl_printer_print_multi_aff(
3731 __isl_take isl_printer *p,
3732 __isl_keep isl_multi_aff *maff);
3733 __isl_give isl_printer *isl_printer_print_pw_aff(
3734 __isl_take isl_printer *p,
3735 __isl_keep isl_pw_aff *pwaff);
3736 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3737 __isl_take isl_printer *p,
3738 __isl_keep isl_pw_multi_aff *pma);
3739 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3740 __isl_take isl_printer *p,
3741 __isl_keep isl_multi_pw_aff *mpa);
3742 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3743 __isl_take isl_printer *p,
3744 __isl_keep isl_union_pw_aff *upa);
3745 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3746 __isl_take isl_printer *p,
3747 __isl_keep isl_union_pw_multi_aff *upma);
3748 __isl_give isl_printer *
3749 isl_printer_print_multi_union_pw_aff(
3750 __isl_take isl_printer *p,
3751 __isl_keep isl_multi_union_pw_aff *mupa);
3753 #include <isl/polynomial.h>
3754 __isl_give isl_printer *isl_printer_print_qpolynomial(
3755 __isl_take isl_printer *p,
3756 __isl_keep isl_qpolynomial *qp);
3757 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3758 __isl_take isl_printer *p,
3759 __isl_keep isl_pw_qpolynomial *pwqp);
3760 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3761 __isl_take isl_printer *p,
3762 __isl_keep isl_union_pw_qpolynomial *upwqp);
3764 __isl_give isl_printer *
3765 isl_printer_print_pw_qpolynomial_fold(
3766 __isl_take isl_printer *p,
3767 __isl_keep isl_pw_qpolynomial_fold *pwf);
3768 __isl_give isl_printer *
3769 isl_printer_print_union_pw_qpolynomial_fold(
3770 __isl_take isl_printer *p,
3771 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3773 For C<isl_printer_print_qpolynomial>,
3774 C<isl_printer_print_pw_qpolynomial> and
3775 C<isl_printer_print_pw_qpolynomial_fold>,
3776 the output format of the printer
3777 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3778 For C<isl_printer_print_union_pw_qpolynomial> and
3779 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3781 In case of printing in C<ISL_FORMAT_C>, the user may want
3782 to set the names of all dimensions first.
3784 C<isl> also provides limited support for printing YAML documents,
3785 just enough for the internal use for printing such documents.
3787 #include <isl/printer.h>
3788 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3789 __isl_take isl_printer *p);
3790 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3791 __isl_take isl_printer *p);
3792 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3793 __isl_take isl_printer *p);
3794 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3795 __isl_take isl_printer *p);
3796 __isl_give isl_printer *isl_printer_yaml_next(
3797 __isl_take isl_printer *p);
3799 A document is started by a call to either
3800 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3801 Anything printed to the printer after such a call belong to the
3802 first key of the mapping or the first element in the sequence.
3803 The function C<isl_printer_yaml_next> moves to the value if
3804 we are currently printing a mapping key, the next key if we
3805 are printing a value or the next element if we are printing
3806 an element in a sequence.
3807 Nested mappings and sequences are initiated by the same
3808 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3809 Each call to these functions needs to have a corresponding call to
3810 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3812 When called on a file printer, the following function flushes
3813 the file. When called on a string printer, the buffer is cleared.
3815 __isl_give isl_printer *isl_printer_flush(
3816 __isl_take isl_printer *p);
3818 The following functions allow the user to attach
3819 notes to a printer in order to keep track of additional state.
3821 #include <isl/printer.h>
3822 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3823 __isl_keep isl_id *id);
3824 __isl_give isl_id *isl_printer_get_note(
3825 __isl_keep isl_printer *p, __isl_take isl_id *id);
3826 __isl_give isl_printer *isl_printer_set_note(
3827 __isl_take isl_printer *p,
3828 __isl_take isl_id *id, __isl_take isl_id *note);
3830 C<isl_printer_set_note> associates the given note to the given
3831 identifier in the printer.
3832 C<isl_printer_get_note> retrieves a note associated to an
3834 C<isl_printer_has_note> checks if there is such a note.
3835 C<isl_printer_get_note> fails if the requested note does not exist.
3837 Alternatively, a string representation can be obtained
3838 directly using the following functions, which always print
3842 __isl_give char *isl_id_to_str(
3843 __isl_keep isl_id *id);
3845 #include <isl/space.h>
3846 __isl_give char *isl_space_to_str(
3847 __isl_keep isl_space *space);
3849 #include <isl/val.h>
3850 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3851 __isl_give char *isl_multi_val_to_str(
3852 __isl_keep isl_multi_val *mv);
3854 #include <isl/set.h>
3855 __isl_give char *isl_basic_set_to_str(
3856 __isl_keep isl_basic_set *bset);
3857 __isl_give char *isl_set_to_str(
3858 __isl_keep isl_set *set);
3860 #include <isl/union_set.h>
3861 __isl_give char *isl_union_set_to_str(
3862 __isl_keep isl_union_set *uset);
3864 #include <isl/map.h>
3865 __isl_give char *isl_basic_map_to_str(
3866 __isl_keep isl_basic_map *bmap);
3867 __isl_give char *isl_map_to_str(
3868 __isl_keep isl_map *map);
3870 #include <isl/union_map.h>
3871 __isl_give char *isl_union_map_to_str(
3872 __isl_keep isl_union_map *umap);
3874 #include <isl/aff.h>
3875 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3876 __isl_give char *isl_pw_aff_to_str(
3877 __isl_keep isl_pw_aff *pa);
3878 __isl_give char *isl_multi_aff_to_str(
3879 __isl_keep isl_multi_aff *ma);
3880 __isl_give char *isl_pw_multi_aff_to_str(
3881 __isl_keep isl_pw_multi_aff *pma);
3882 __isl_give char *isl_multi_pw_aff_to_str(
3883 __isl_keep isl_multi_pw_aff *mpa);
3884 __isl_give char *isl_union_pw_aff_to_str(
3885 __isl_keep isl_union_pw_aff *upa);
3886 __isl_give char *isl_union_pw_multi_aff_to_str(
3887 __isl_keep isl_union_pw_multi_aff *upma);
3888 __isl_give char *isl_multi_union_pw_aff_to_str(
3889 __isl_keep isl_multi_union_pw_aff *mupa);
3891 #include <isl/point.h>
3892 __isl_give char *isl_point_to_str(
3893 __isl_keep isl_point *pnt);
3895 #include <isl/polynomial.h>
3896 __isl_give char *isl_pw_qpolynomial_to_str(
3897 __isl_keep isl_pw_qpolynomial *pwqp);
3898 __isl_give char *isl_union_pw_qpolynomial_to_str(
3899 __isl_keep isl_union_pw_qpolynomial *upwqp);
3903 =head3 Unary Properties
3909 The following functions test whether the given set or relation
3910 contains any integer points. The ``plain'' variants do not perform
3911 any computations, but simply check if the given set or relation
3912 is already known to be empty.
3914 #include <isl/set.h>
3915 isl_bool isl_basic_set_plain_is_empty(
3916 __isl_keep isl_basic_set *bset);
3917 isl_bool isl_basic_set_is_empty(
3918 __isl_keep isl_basic_set *bset);
3919 isl_bool isl_set_plain_is_empty(
3920 __isl_keep isl_set *set);
3921 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3923 #include <isl/union_set.h>
3924 isl_bool isl_union_set_is_empty(
3925 __isl_keep isl_union_set *uset);
3927 #include <isl/map.h>
3928 isl_bool isl_basic_map_plain_is_empty(
3929 __isl_keep isl_basic_map *bmap);
3930 isl_bool isl_basic_map_is_empty(
3931 __isl_keep isl_basic_map *bmap);
3932 isl_bool isl_map_plain_is_empty(
3933 __isl_keep isl_map *map);
3934 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3936 #include <isl/union_map.h>
3937 isl_bool isl_union_map_plain_is_empty(
3938 __isl_keep isl_union_map *umap);
3939 isl_bool isl_union_map_is_empty(
3940 __isl_keep isl_union_map *umap);
3942 =item * Universality
3944 isl_bool isl_basic_set_plain_is_universe(
3945 __isl_keep isl_basic_set *bset);
3946 isl_bool isl_basic_set_is_universe(
3947 __isl_keep isl_basic_set *bset);
3948 isl_bool isl_basic_map_plain_is_universe(
3949 __isl_keep isl_basic_map *bmap);
3950 isl_bool isl_basic_map_is_universe(
3951 __isl_keep isl_basic_map *bmap);
3952 isl_bool isl_set_plain_is_universe(
3953 __isl_keep isl_set *set);
3954 isl_bool isl_map_plain_is_universe(
3955 __isl_keep isl_map *map);
3957 =item * Single-valuedness
3959 #include <isl/set.h>
3960 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3962 #include <isl/map.h>
3963 isl_bool isl_basic_map_is_single_valued(
3964 __isl_keep isl_basic_map *bmap);
3965 isl_bool isl_map_plain_is_single_valued(
3966 __isl_keep isl_map *map);
3967 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3969 #include <isl/union_map.h>
3970 isl_bool isl_union_map_is_single_valued(
3971 __isl_keep isl_union_map *umap);
3975 isl_bool isl_map_plain_is_injective(
3976 __isl_keep isl_map *map);
3977 isl_bool isl_map_is_injective(
3978 __isl_keep isl_map *map);
3979 isl_bool isl_union_map_plain_is_injective(
3980 __isl_keep isl_union_map *umap);
3981 isl_bool isl_union_map_is_injective(
3982 __isl_keep isl_union_map *umap);
3986 isl_bool isl_map_is_bijective(
3987 __isl_keep isl_map *map);
3988 isl_bool isl_union_map_is_bijective(
3989 __isl_keep isl_union_map *umap);
3993 The following functions test whether the given relation
3994 only maps elements to themselves.
3996 #include <isl/map.h>
3997 isl_bool isl_map_is_identity(
3998 __isl_keep isl_map *map);
4000 #include <isl/union_map.h>
4001 isl_bool isl_union_map_is_identity(
4002 __isl_keep isl_union_map *umap);
4006 __isl_give isl_val *
4007 isl_basic_map_plain_get_val_if_fixed(
4008 __isl_keep isl_basic_map *bmap,
4009 enum isl_dim_type type, unsigned pos);
4010 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4011 __isl_keep isl_set *set,
4012 enum isl_dim_type type, unsigned pos);
4013 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4014 __isl_keep isl_map *map,
4015 enum isl_dim_type type, unsigned pos);
4017 If the set or relation obviously lies on a hyperplane where the given dimension
4018 has a fixed value, then return that value.
4019 Otherwise return NaN.
4023 isl_stat isl_set_dim_residue_class_val(
4024 __isl_keep isl_set *set,
4025 int pos, __isl_give isl_val **modulo,
4026 __isl_give isl_val **residue);
4028 Check if the values of the given set dimension are equal to a fixed
4029 value modulo some integer value. If so, assign the modulo to C<*modulo>
4030 and the fixed value to C<*residue>. If the given dimension attains only
4031 a single value, then assign C<0> to C<*modulo> and the fixed value to
4033 If the dimension does not attain only a single value and if no modulo
4034 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4036 #include <isl/set.h>
4037 __isl_give isl_stride_info *isl_set_get_stride_info(
4038 __isl_keep isl_set *set, int pos);
4039 __isl_give isl_val *isl_set_get_stride(
4040 __isl_keep isl_set *set, int pos);
4042 #include <isl/map.h>
4043 __isl_give isl_stride_info *
4044 isl_map_get_range_stride_info(
4045 __isl_keep isl_map *map, int pos);
4047 Check if the values of the given set dimension are equal to
4048 some affine expression of the other dimensions (the offset)
4049 modulo some integer stride or
4050 check if the values of the given output dimensions are equal to
4051 some affine expression of the input dimensions (the offset)
4052 modulo some integer stride.
4053 If no more specific information can be found, then the stride
4054 is taken to be one and the offset is taken to be the zero expression.
4055 The function C<isl_set_get_stride> performs the same
4056 computation as C<isl_set_get_stride_info> but only returns the stride.
4057 For the other functions,
4058 the stride and offset can be extracted from the returned object
4059 using the following functions.
4061 #include <isl/stride_info.h>
4062 __isl_give isl_val *isl_stride_info_get_stride(
4063 __isl_keep isl_stride_info *si);
4064 __isl_give isl_aff *isl_stride_info_get_offset(
4065 __isl_keep isl_stride_info *si);
4067 The stride info object can be copied and released using the following
4070 #include <isl/stride_info.h>
4071 __isl_give isl_stride_info *isl_stride_info_copy(
4072 __isl_keep isl_stride_info *si);
4073 __isl_null isl_stride_info *isl_stride_info_free(
4074 __isl_take isl_stride_info *si);
4078 To check whether the description of a set, relation or function depends
4079 on one or more given dimensions,
4080 the following functions can be used.
4082 #include <isl/constraint.h>
4083 isl_bool isl_constraint_involves_dims(
4084 __isl_keep isl_constraint *constraint,
4085 enum isl_dim_type type, unsigned first, unsigned n);
4087 #include <isl/set.h>
4088 isl_bool isl_basic_set_involves_dims(
4089 __isl_keep isl_basic_set *bset,
4090 enum isl_dim_type type, unsigned first, unsigned n);
4091 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4092 enum isl_dim_type type, unsigned first, unsigned n);
4094 #include <isl/map.h>
4095 isl_bool isl_basic_map_involves_dims(
4096 __isl_keep isl_basic_map *bmap,
4097 enum isl_dim_type type, unsigned first, unsigned n);
4098 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4099 enum isl_dim_type type, unsigned first, unsigned n);
4101 #include <isl/union_map.h>
4102 isl_bool isl_union_map_involves_dims(
4103 __isl_keep isl_union_map *umap,
4104 enum isl_dim_type type, unsigned first, unsigned n);
4106 #include <isl/aff.h>
4107 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4108 enum isl_dim_type type, unsigned first, unsigned n);
4109 isl_bool isl_pw_aff_involves_dims(
4110 __isl_keep isl_pw_aff *pwaff,
4111 enum isl_dim_type type, unsigned first, unsigned n);
4112 isl_bool isl_multi_aff_involves_dims(
4113 __isl_keep isl_multi_aff *ma,
4114 enum isl_dim_type type, unsigned first, unsigned n);
4115 isl_bool isl_pw_multi_aff_involves_dims(
4116 __isl_keep isl_pw_multi_aff *pma,
4117 enum isl_dim_type type, unsigned first, unsigned n);
4118 isl_bool isl_multi_pw_aff_involves_dims(
4119 __isl_keep isl_multi_pw_aff *mpa,
4120 enum isl_dim_type type, unsigned first, unsigned n);
4122 #include <isl/polynomial.h>
4123 isl_bool isl_qpolynomial_involves_dims(
4124 __isl_keep isl_qpolynomial *qp,
4125 enum isl_dim_type type, unsigned first, unsigned n);
4127 Similarly, the following functions can be used to check whether
4128 a given dimension is involved in any lower or upper bound.
4130 #include <isl/set.h>
4131 isl_bool isl_set_dim_has_any_lower_bound(
4132 __isl_keep isl_set *set,
4133 enum isl_dim_type type, unsigned pos);
4134 isl_bool isl_set_dim_has_any_upper_bound(
4135 __isl_keep isl_set *set,
4136 enum isl_dim_type type, unsigned pos);
4138 Note that these functions return true even if there is a bound on
4139 the dimension on only some of the basic sets of C<set>.
4140 To check if they have a bound for all of the basic sets in C<set>,
4141 use the following functions instead.
4143 #include <isl/set.h>
4144 isl_bool isl_set_dim_has_lower_bound(
4145 __isl_keep isl_set *set,
4146 enum isl_dim_type type, unsigned pos);
4147 isl_bool isl_set_dim_has_upper_bound(
4148 __isl_keep isl_set *set,
4149 enum isl_dim_type type, unsigned pos);
4153 To check whether a set is a parameter domain, use this function:
4155 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4156 isl_bool isl_union_set_is_params(
4157 __isl_keep isl_union_set *uset);
4161 The following functions check whether the space of the given
4162 (basic) set or relation domain and/or range is a wrapped relation.
4164 #include <isl/space.h>
4165 isl_bool isl_space_is_wrapping(
4166 __isl_keep isl_space *space);
4167 isl_bool isl_space_domain_is_wrapping(
4168 __isl_keep isl_space *space);
4169 isl_bool isl_space_range_is_wrapping(
4170 __isl_keep isl_space *space);
4171 isl_bool isl_space_is_product(
4172 __isl_keep isl_space *space);
4174 #include <isl/set.h>
4175 isl_bool isl_basic_set_is_wrapping(
4176 __isl_keep isl_basic_set *bset);
4177 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4179 #include <isl/map.h>
4180 isl_bool isl_map_domain_is_wrapping(
4181 __isl_keep isl_map *map);
4182 isl_bool isl_map_range_is_wrapping(
4183 __isl_keep isl_map *map);
4184 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4186 #include <isl/val.h>
4187 isl_bool isl_multi_val_range_is_wrapping(
4188 __isl_keep isl_multi_val *mv);
4190 #include <isl/aff.h>
4191 isl_bool isl_multi_aff_range_is_wrapping(
4192 __isl_keep isl_multi_aff *ma);
4193 isl_bool isl_multi_pw_aff_range_is_wrapping(
4194 __isl_keep isl_multi_pw_aff *mpa);
4195 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4196 __isl_keep isl_multi_union_pw_aff *mupa);
4198 The input to C<isl_space_is_wrapping> should
4199 be the space of a set, while that of
4200 C<isl_space_domain_is_wrapping> and
4201 C<isl_space_range_is_wrapping> should be the space of a relation.
4202 The input to C<isl_space_is_product> can be either the space
4203 of a set or that of a binary relation.
4204 In case the input is the space of a binary relation, it checks
4205 whether both domain and range are wrapping.
4207 =item * Internal Product
4209 isl_bool isl_basic_map_can_zip(
4210 __isl_keep isl_basic_map *bmap);
4211 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4213 Check whether the product of domain and range of the given relation
4215 i.e., whether both domain and range are nested relations.
4219 #include <isl/space.h>
4220 isl_bool isl_space_can_curry(
4221 __isl_keep isl_space *space);
4223 #include <isl/map.h>
4224 isl_bool isl_basic_map_can_curry(
4225 __isl_keep isl_basic_map *bmap);
4226 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4228 Check whether the domain of the (basic) relation is a wrapped relation.
4230 #include <isl/space.h>
4231 __isl_give isl_space *isl_space_uncurry(
4232 __isl_take isl_space *space);
4234 #include <isl/map.h>
4235 isl_bool isl_basic_map_can_uncurry(
4236 __isl_keep isl_basic_map *bmap);
4237 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4239 Check whether the range of the (basic) relation is a wrapped relation.
4241 #include <isl/space.h>
4242 isl_bool isl_space_can_range_curry(
4243 __isl_keep isl_space *space);
4245 #include <isl/map.h>
4246 isl_bool isl_map_can_range_curry(
4247 __isl_keep isl_map *map);
4249 Check whether the domain of the relation wrapped in the range of
4250 the input is itself a wrapped relation.
4252 =item * Special Values
4254 #include <isl/aff.h>
4255 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4256 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4257 isl_bool isl_multi_pw_aff_is_cst(
4258 __isl_keep isl_multi_pw_aff *mpa);
4260 Check whether the given expression is a constant.
4262 #include <isl/val.h>
4263 isl_bool isl_multi_val_involves_nan(
4264 __isl_keep isl_multi_val *mv);
4266 #include <isl/aff.h>
4267 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4268 isl_bool isl_multi_aff_involves_nan(
4269 __isl_keep isl_multi_aff *ma);
4270 isl_bool isl_pw_aff_involves_nan(
4271 __isl_keep isl_pw_aff *pa);
4272 isl_bool isl_pw_multi_aff_involves_nan(
4273 __isl_keep isl_pw_multi_aff *pma);
4274 isl_bool isl_multi_pw_aff_involves_nan(
4275 __isl_keep isl_multi_pw_aff *mpa);
4276 isl_bool isl_union_pw_aff_involves_nan(
4277 __isl_keep isl_union_pw_aff *upa);
4278 isl_bool isl_union_pw_multi_aff_involves_nan(
4279 __isl_keep isl_union_pw_multi_aff *upma);
4280 isl_bool isl_multi_union_pw_aff_involves_nan(
4281 __isl_keep isl_multi_union_pw_aff *mupa);
4283 #include <isl/polynomial.h>
4284 isl_bool isl_qpolynomial_is_nan(
4285 __isl_keep isl_qpolynomial *qp);
4286 isl_bool isl_qpolynomial_fold_is_nan(
4287 __isl_keep isl_qpolynomial_fold *fold);
4288 isl_bool isl_pw_qpolynomial_involves_nan(
4289 __isl_keep isl_pw_qpolynomial *pwqp);
4290 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4291 __isl_keep isl_pw_qpolynomial_fold *pwf);
4292 isl_bool isl_union_pw_qpolynomial_involves_nan(
4293 __isl_keep isl_union_pw_qpolynomial *upwqp);
4294 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4295 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4297 Check whether the given expression is equal to or involves NaN.
4299 #include <isl/aff.h>
4300 isl_bool isl_aff_plain_is_zero(
4301 __isl_keep isl_aff *aff);
4303 Check whether the affine expression is obviously zero.
4307 =head3 Binary Properties
4313 The following functions check whether two objects
4314 represent the same set, relation or function.
4315 The C<plain> variants only return true if the objects
4316 are obviously the same. That is, they may return false
4317 even if the objects are the same, but they will never
4318 return true if the objects are not the same.
4320 #include <isl/set.h>
4321 isl_bool isl_basic_set_plain_is_equal(
4322 __isl_keep isl_basic_set *bset1,
4323 __isl_keep isl_basic_set *bset2);
4324 isl_bool isl_basic_set_is_equal(
4325 __isl_keep isl_basic_set *bset1,
4326 __isl_keep isl_basic_set *bset2);
4327 isl_bool isl_set_plain_is_equal(
4328 __isl_keep isl_set *set1,
4329 __isl_keep isl_set *set2);
4330 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4331 __isl_keep isl_set *set2);
4333 #include <isl/map.h>
4334 isl_bool isl_basic_map_is_equal(
4335 __isl_keep isl_basic_map *bmap1,
4336 __isl_keep isl_basic_map *bmap2);
4337 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4338 __isl_keep isl_map *map2);
4339 isl_bool isl_map_plain_is_equal(
4340 __isl_keep isl_map *map1,
4341 __isl_keep isl_map *map2);
4343 #include <isl/union_set.h>
4344 isl_bool isl_union_set_is_equal(
4345 __isl_keep isl_union_set *uset1,
4346 __isl_keep isl_union_set *uset2);
4348 #include <isl/union_map.h>
4349 isl_bool isl_union_map_is_equal(
4350 __isl_keep isl_union_map *umap1,
4351 __isl_keep isl_union_map *umap2);
4353 #include <isl/val.h>
4354 isl_bool isl_multi_val_plain_is_equal(
4355 __isl_keep isl_multi_val *mv1,
4356 __isl_keep isl_multi_val *mv2);
4358 #include <isl/aff.h>
4359 isl_bool isl_aff_plain_is_equal(
4360 __isl_keep isl_aff *aff1,
4361 __isl_keep isl_aff *aff2);
4362 isl_bool isl_multi_aff_plain_is_equal(
4363 __isl_keep isl_multi_aff *maff1,
4364 __isl_keep isl_multi_aff *maff2);
4365 isl_bool isl_pw_aff_plain_is_equal(
4366 __isl_keep isl_pw_aff *pwaff1,
4367 __isl_keep isl_pw_aff *pwaff2);
4368 isl_bool isl_pw_aff_is_equal(
4369 __isl_keep isl_pw_aff *pa1,
4370 __isl_keep isl_pw_aff *pa2);
4371 isl_bool isl_pw_multi_aff_plain_is_equal(
4372 __isl_keep isl_pw_multi_aff *pma1,
4373 __isl_keep isl_pw_multi_aff *pma2);
4374 isl_bool isl_pw_multi_aff_is_equal(
4375 __isl_keep isl_pw_multi_aff *pma1,
4376 __isl_keep isl_pw_multi_aff *pma2);
4377 isl_bool isl_multi_pw_aff_plain_is_equal(
4378 __isl_keep isl_multi_pw_aff *mpa1,
4379 __isl_keep isl_multi_pw_aff *mpa2);
4380 isl_bool isl_multi_pw_aff_is_equal(
4381 __isl_keep isl_multi_pw_aff *mpa1,
4382 __isl_keep isl_multi_pw_aff *mpa2);
4383 isl_bool isl_union_pw_aff_plain_is_equal(
4384 __isl_keep isl_union_pw_aff *upa1,
4385 __isl_keep isl_union_pw_aff *upa2);
4386 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4387 __isl_keep isl_union_pw_multi_aff *upma1,
4388 __isl_keep isl_union_pw_multi_aff *upma2);
4389 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4390 __isl_keep isl_multi_union_pw_aff *mupa1,
4391 __isl_keep isl_multi_union_pw_aff *mupa2);
4393 #include <isl/polynomial.h>
4394 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4395 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4396 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4397 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4398 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4399 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4401 =item * Disjointness
4403 #include <isl/set.h>
4404 isl_bool isl_basic_set_is_disjoint(
4405 __isl_keep isl_basic_set *bset1,
4406 __isl_keep isl_basic_set *bset2);
4407 isl_bool isl_set_plain_is_disjoint(
4408 __isl_keep isl_set *set1,
4409 __isl_keep isl_set *set2);
4410 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4411 __isl_keep isl_set *set2);
4413 #include <isl/map.h>
4414 isl_bool isl_basic_map_is_disjoint(
4415 __isl_keep isl_basic_map *bmap1,
4416 __isl_keep isl_basic_map *bmap2);
4417 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4418 __isl_keep isl_map *map2);
4420 #include <isl/union_set.h>
4421 isl_bool isl_union_set_is_disjoint(
4422 __isl_keep isl_union_set *uset1,
4423 __isl_keep isl_union_set *uset2);
4425 #include <isl/union_map.h>
4426 isl_bool isl_union_map_is_disjoint(
4427 __isl_keep isl_union_map *umap1,
4428 __isl_keep isl_union_map *umap2);
4432 isl_bool isl_basic_set_is_subset(
4433 __isl_keep isl_basic_set *bset1,
4434 __isl_keep isl_basic_set *bset2);
4435 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4436 __isl_keep isl_set *set2);
4437 isl_bool isl_set_is_strict_subset(
4438 __isl_keep isl_set *set1,
4439 __isl_keep isl_set *set2);
4440 isl_bool isl_union_set_is_subset(
4441 __isl_keep isl_union_set *uset1,
4442 __isl_keep isl_union_set *uset2);
4443 isl_bool isl_union_set_is_strict_subset(
4444 __isl_keep isl_union_set *uset1,
4445 __isl_keep isl_union_set *uset2);
4446 isl_bool isl_basic_map_is_subset(
4447 __isl_keep isl_basic_map *bmap1,
4448 __isl_keep isl_basic_map *bmap2);
4449 isl_bool isl_basic_map_is_strict_subset(
4450 __isl_keep isl_basic_map *bmap1,
4451 __isl_keep isl_basic_map *bmap2);
4452 isl_bool isl_map_is_subset(
4453 __isl_keep isl_map *map1,
4454 __isl_keep isl_map *map2);
4455 isl_bool isl_map_is_strict_subset(
4456 __isl_keep isl_map *map1,
4457 __isl_keep isl_map *map2);
4458 isl_bool isl_union_map_is_subset(
4459 __isl_keep isl_union_map *umap1,
4460 __isl_keep isl_union_map *umap2);
4461 isl_bool isl_union_map_is_strict_subset(
4462 __isl_keep isl_union_map *umap1,
4463 __isl_keep isl_union_map *umap2);
4465 Check whether the first argument is a (strict) subset of the
4470 Every comparison function returns a negative value if the first
4471 argument is considered smaller than the second, a positive value
4472 if the first argument is considered greater and zero if the two
4473 constraints are considered the same by the comparison criterion.
4475 #include <isl/constraint.h>
4476 int isl_constraint_plain_cmp(
4477 __isl_keep isl_constraint *c1,
4478 __isl_keep isl_constraint *c2);
4480 This function is useful for sorting C<isl_constraint>s.
4481 The order depends on the internal representation of the inputs.
4482 The order is fixed over different calls to the function (assuming
4483 the internal representation of the inputs has not changed), but may
4484 change over different versions of C<isl>.
4486 #include <isl/constraint.h>
4487 int isl_constraint_cmp_last_non_zero(
4488 __isl_keep isl_constraint *c1,
4489 __isl_keep isl_constraint *c2);
4491 This function can be used to sort constraints that live in the same
4492 local space. Constraints that involve ``earlier'' dimensions or
4493 that have a smaller coefficient for the shared latest dimension
4494 are considered smaller than other constraints.
4495 This function only defines a B<partial> order.
4497 #include <isl/set.h>
4498 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4499 __isl_keep isl_set *set2);
4501 This function is useful for sorting C<isl_set>s.
4502 The order depends on the internal representation of the inputs.
4503 The order is fixed over different calls to the function (assuming
4504 the internal representation of the inputs has not changed), but may
4505 change over different versions of C<isl>.
4507 #include <isl/aff.h>
4508 int isl_multi_aff_plain_cmp(
4509 __isl_keep isl_multi_aff *ma1,
4510 __isl_keep isl_multi_aff *ma2);
4511 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4512 __isl_keep isl_pw_aff *pa2);
4514 The functions C<isl_multi_aff_plain_cmp> and
4515 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4516 C<isl_pw_aff>s. The order is not strictly defined.
4517 The current order sorts expressions that only involve
4518 earlier dimensions before those that involve later dimensions.
4522 =head2 Unary Operations
4528 __isl_give isl_set *isl_set_complement(
4529 __isl_take isl_set *set);
4530 __isl_give isl_map *isl_map_complement(
4531 __isl_take isl_map *map);
4535 #include <isl/space.h>
4536 __isl_give isl_space *isl_space_reverse(
4537 __isl_take isl_space *space);
4539 #include <isl/map.h>
4540 __isl_give isl_basic_map *isl_basic_map_reverse(
4541 __isl_take isl_basic_map *bmap);
4542 __isl_give isl_map *isl_map_reverse(
4543 __isl_take isl_map *map);
4545 #include <isl/union_map.h>
4546 __isl_give isl_union_map *isl_union_map_reverse(
4547 __isl_take isl_union_map *umap);
4551 #include <isl/space.h>
4552 __isl_give isl_space *isl_space_domain(
4553 __isl_take isl_space *space);
4554 __isl_give isl_space *isl_space_range(
4555 __isl_take isl_space *space);
4556 __isl_give isl_space *isl_space_params(
4557 __isl_take isl_space *space);
4559 #include <isl/local_space.h>
4560 __isl_give isl_local_space *isl_local_space_domain(
4561 __isl_take isl_local_space *ls);
4562 __isl_give isl_local_space *isl_local_space_range(
4563 __isl_take isl_local_space *ls);
4565 #include <isl/set.h>
4566 __isl_give isl_basic_set *isl_basic_set_project_out(
4567 __isl_take isl_basic_set *bset,
4568 enum isl_dim_type type, unsigned first, unsigned n);
4569 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4570 enum isl_dim_type type, unsigned first, unsigned n);
4571 __isl_give isl_map *isl_set_project_onto_map(
4572 __isl_take isl_set *set,
4573 enum isl_dim_type type, unsigned first,
4575 __isl_give isl_basic_set *isl_basic_set_params(
4576 __isl_take isl_basic_set *bset);
4577 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4579 The function C<isl_set_project_onto_map> returns a relation
4580 that projects the input set onto the given set dimensions.
4582 #include <isl/map.h>
4583 __isl_give isl_basic_map *isl_basic_map_project_out(
4584 __isl_take isl_basic_map *bmap,
4585 enum isl_dim_type type, unsigned first, unsigned n);
4586 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4587 enum isl_dim_type type, unsigned first, unsigned n);
4588 __isl_give isl_basic_set *isl_basic_map_domain(
4589 __isl_take isl_basic_map *bmap);
4590 __isl_give isl_basic_set *isl_basic_map_range(
4591 __isl_take isl_basic_map *bmap);
4592 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4593 __isl_give isl_set *isl_map_domain(
4594 __isl_take isl_map *bmap);
4595 __isl_give isl_set *isl_map_range(
4596 __isl_take isl_map *map);
4598 #include <isl/union_set.h>
4599 __isl_give isl_union_set *isl_union_set_project_out(
4600 __isl_take isl_union_set *uset,
4601 enum isl_dim_type type,
4602 unsigned first, unsigned n);
4603 __isl_give isl_set *isl_union_set_params(
4604 __isl_take isl_union_set *uset);
4606 The function C<isl_union_set_project_out> can only project out
4609 #include <isl/union_map.h>
4610 __isl_give isl_union_map *isl_union_map_project_out(
4611 __isl_take isl_union_map *umap,
4612 enum isl_dim_type type, unsigned first, unsigned n);
4613 __isl_give isl_union_map *
4614 isl_union_map_project_out_all_params(
4615 __isl_take isl_union_map *umap);
4616 __isl_give isl_set *isl_union_map_params(
4617 __isl_take isl_union_map *umap);
4618 __isl_give isl_union_set *isl_union_map_domain(
4619 __isl_take isl_union_map *umap);
4620 __isl_give isl_union_set *isl_union_map_range(
4621 __isl_take isl_union_map *umap);
4623 The function C<isl_union_map_project_out> can only project out
4626 #include <isl/aff.h>
4627 __isl_give isl_aff *isl_aff_project_domain_on_params(
4628 __isl_take isl_aff *aff);
4629 __isl_give isl_multi_aff *
4630 isl_multi_aff_project_domain_on_params(
4631 __isl_take isl_multi_aff *ma);
4632 __isl_give isl_pw_aff *
4633 isl_pw_aff_project_domain_on_params(
4634 __isl_take isl_pw_aff *pa);
4635 __isl_give isl_multi_pw_aff *
4636 isl_multi_pw_aff_project_domain_on_params(
4637 __isl_take isl_multi_pw_aff *mpa);
4638 __isl_give isl_pw_multi_aff *
4639 isl_pw_multi_aff_project_domain_on_params(
4640 __isl_take isl_pw_multi_aff *pma);
4641 __isl_give isl_set *isl_pw_aff_domain(
4642 __isl_take isl_pw_aff *pwaff);
4643 __isl_give isl_set *isl_pw_multi_aff_domain(
4644 __isl_take isl_pw_multi_aff *pma);
4645 __isl_give isl_set *isl_multi_pw_aff_domain(
4646 __isl_take isl_multi_pw_aff *mpa);
4647 __isl_give isl_union_set *isl_union_pw_aff_domain(
4648 __isl_take isl_union_pw_aff *upa);
4649 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4650 __isl_take isl_union_pw_multi_aff *upma);
4651 __isl_give isl_union_set *
4652 isl_multi_union_pw_aff_domain(
4653 __isl_take isl_multi_union_pw_aff *mupa);
4654 __isl_give isl_set *isl_pw_aff_params(
4655 __isl_take isl_pw_aff *pwa);
4657 If no explicit domain was set on a zero-dimensional input to
4658 C<isl_multi_union_pw_aff_domain>, then this function will
4659 return a parameter set.
4661 #include <isl/polynomial.h>
4662 __isl_give isl_qpolynomial *
4663 isl_qpolynomial_project_domain_on_params(
4664 __isl_take isl_qpolynomial *qp);
4665 __isl_give isl_pw_qpolynomial *
4666 isl_pw_qpolynomial_project_domain_on_params(
4667 __isl_take isl_pw_qpolynomial *pwqp);
4668 __isl_give isl_pw_qpolynomial_fold *
4669 isl_pw_qpolynomial_fold_project_domain_on_params(
4670 __isl_take isl_pw_qpolynomial_fold *pwf);
4671 __isl_give isl_set *isl_pw_qpolynomial_domain(
4672 __isl_take isl_pw_qpolynomial *pwqp);
4673 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4674 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4675 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4676 __isl_take isl_union_pw_qpolynomial *upwqp);
4678 #include <isl/space.h>
4679 __isl_give isl_space *isl_space_domain_map(
4680 __isl_take isl_space *space);
4681 __isl_give isl_space *isl_space_range_map(
4682 __isl_take isl_space *space);
4684 #include <isl/map.h>
4685 __isl_give isl_map *isl_set_wrapped_domain_map(
4686 __isl_take isl_set *set);
4687 __isl_give isl_basic_map *isl_basic_map_domain_map(
4688 __isl_take isl_basic_map *bmap);
4689 __isl_give isl_basic_map *isl_basic_map_range_map(
4690 __isl_take isl_basic_map *bmap);
4691 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4692 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4694 #include <isl/union_map.h>
4695 __isl_give isl_union_map *isl_union_map_domain_map(
4696 __isl_take isl_union_map *umap);
4697 __isl_give isl_union_pw_multi_aff *
4698 isl_union_map_domain_map_union_pw_multi_aff(
4699 __isl_take isl_union_map *umap);
4700 __isl_give isl_union_map *isl_union_map_range_map(
4701 __isl_take isl_union_map *umap);
4702 __isl_give isl_union_map *
4703 isl_union_set_wrapped_domain_map(
4704 __isl_take isl_union_set *uset);
4706 The functions above construct a (basic, regular or union) relation
4707 that maps (a wrapped version of) the input relation to its domain or range.
4708 C<isl_set_wrapped_domain_map> maps the input set to the domain
4709 of its wrapped relation.
4713 __isl_give isl_basic_set *isl_basic_set_eliminate(
4714 __isl_take isl_basic_set *bset,
4715 enum isl_dim_type type,
4716 unsigned first, unsigned n);
4717 __isl_give isl_set *isl_set_eliminate(
4718 __isl_take isl_set *set, enum isl_dim_type type,
4719 unsigned first, unsigned n);
4720 __isl_give isl_basic_map *isl_basic_map_eliminate(
4721 __isl_take isl_basic_map *bmap,
4722 enum isl_dim_type type,
4723 unsigned first, unsigned n);
4724 __isl_give isl_map *isl_map_eliminate(
4725 __isl_take isl_map *map, enum isl_dim_type type,
4726 unsigned first, unsigned n);
4728 Eliminate the coefficients for the given dimensions from the constraints,
4729 without removing the dimensions.
4731 =item * Constructing a set from a parameter domain
4733 A zero-dimensional (local) space or (basic) set can be constructed
4734 on a given parameter domain using the following functions.
4736 #include <isl/space.h>
4737 __isl_give isl_space *isl_space_set_from_params(
4738 __isl_take isl_space *space);
4740 #include <isl/local_space.h>
4741 __isl_give isl_local_space *
4742 isl_local_space_set_from_params(
4743 __isl_take isl_local_space *ls);
4745 #include <isl/set.h>
4746 __isl_give isl_basic_set *isl_basic_set_from_params(
4747 __isl_take isl_basic_set *bset);
4748 __isl_give isl_set *isl_set_from_params(
4749 __isl_take isl_set *set);
4751 =item * Constructing a relation from one or two sets
4753 Create a relation with the given set(s) as domain and/or range.
4754 If only the domain or the range is specified, then
4755 the range or domain of the created relation is a zero-dimensional
4756 flat anonymous space.
4758 #include <isl/space.h>
4759 __isl_give isl_space *isl_space_from_domain(
4760 __isl_take isl_space *space);
4761 __isl_give isl_space *isl_space_from_range(
4762 __isl_take isl_space *space);
4763 __isl_give isl_space *isl_space_map_from_set(
4764 __isl_take isl_space *space);
4765 __isl_give isl_space *isl_space_map_from_domain_and_range(
4766 __isl_take isl_space *domain,
4767 __isl_take isl_space *range);
4769 #include <isl/local_space.h>
4770 __isl_give isl_local_space *isl_local_space_from_domain(
4771 __isl_take isl_local_space *ls);
4773 #include <isl/map.h>
4774 __isl_give isl_map *isl_map_from_domain(
4775 __isl_take isl_set *set);
4776 __isl_give isl_map *isl_map_from_range(
4777 __isl_take isl_set *set);
4779 #include <isl/union_map.h>
4780 __isl_give isl_union_map *isl_union_map_from_domain(
4781 __isl_take isl_union_set *uset);
4782 __isl_give isl_union_map *isl_union_map_from_range(
4783 __isl_take isl_union_set *uset);
4784 __isl_give isl_union_map *
4785 isl_union_map_from_domain_and_range(
4786 __isl_take isl_union_set *domain,
4787 __isl_take isl_union_set *range);
4789 #include <isl/val.h>
4790 __isl_give isl_multi_val *isl_multi_val_from_range(
4791 __isl_take isl_multi_val *mv);
4793 #include <isl/aff.h>
4794 __isl_give isl_aff *isl_aff_from_range(
4795 __isl_take isl_aff *aff);
4796 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4797 __isl_take isl_multi_aff *ma);
4798 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4799 __isl_take isl_pw_aff *pwa);
4800 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4801 __isl_take isl_multi_pw_aff *mpa);
4802 __isl_give isl_multi_union_pw_aff *
4803 isl_multi_union_pw_aff_from_range(
4804 __isl_take isl_multi_union_pw_aff *mupa);
4805 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4806 __isl_take isl_set *set);
4807 __isl_give isl_union_pw_multi_aff *
4808 isl_union_pw_multi_aff_from_domain(
4809 __isl_take isl_union_set *uset);
4811 #include <isl/polynomial.h>
4812 __isl_give isl_pw_qpolynomial *
4813 isl_pw_qpolynomial_from_range(
4814 __isl_take isl_pw_qpolynomial *pwqp);
4815 __isl_give isl_pw_qpolynomial_fold *
4816 isl_pw_qpolynomial_fold_from_range(
4817 __isl_take isl_pw_qpolynomial_fold *pwf);
4821 #include <isl/set.h>
4822 __isl_give isl_basic_set *isl_basic_set_fix_si(
4823 __isl_take isl_basic_set *bset,
4824 enum isl_dim_type type, unsigned pos, int value);
4825 __isl_give isl_basic_set *isl_basic_set_fix_val(
4826 __isl_take isl_basic_set *bset,
4827 enum isl_dim_type type, unsigned pos,
4828 __isl_take isl_val *v);
4829 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4830 enum isl_dim_type type, unsigned pos, int value);
4831 __isl_give isl_set *isl_set_fix_val(
4832 __isl_take isl_set *set,
4833 enum isl_dim_type type, unsigned pos,
4834 __isl_take isl_val *v);
4836 #include <isl/map.h>
4837 __isl_give isl_basic_map *isl_basic_map_fix_si(
4838 __isl_take isl_basic_map *bmap,
4839 enum isl_dim_type type, unsigned pos, int value);
4840 __isl_give isl_basic_map *isl_basic_map_fix_val(
4841 __isl_take isl_basic_map *bmap,
4842 enum isl_dim_type type, unsigned pos,
4843 __isl_take isl_val *v);
4844 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4845 enum isl_dim_type type, unsigned pos, int value);
4846 __isl_give isl_map *isl_map_fix_val(
4847 __isl_take isl_map *map,
4848 enum isl_dim_type type, unsigned pos,
4849 __isl_take isl_val *v);
4851 #include <isl/aff.h>
4852 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4853 __isl_take isl_pw_multi_aff *pma,
4854 enum isl_dim_type type, unsigned pos, int value);
4856 #include <isl/polynomial.h>
4857 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4858 __isl_take isl_pw_qpolynomial *pwqp,
4859 enum isl_dim_type type, unsigned n,
4860 __isl_take isl_val *v);
4861 __isl_give isl_pw_qpolynomial_fold *
4862 isl_pw_qpolynomial_fold_fix_val(
4863 __isl_take isl_pw_qpolynomial_fold *pwf,
4864 enum isl_dim_type type, unsigned n,
4865 __isl_take isl_val *v);
4867 Intersect the set, relation or function domain
4868 with the hyperplane where the given
4869 dimension has the fixed given value.
4871 #include <isl/set.h>
4872 __isl_give isl_basic_set *
4873 isl_basic_set_lower_bound_val(
4874 __isl_take isl_basic_set *bset,
4875 enum isl_dim_type type, unsigned pos,
4876 __isl_take isl_val *value);
4877 __isl_give isl_basic_set *
4878 isl_basic_set_upper_bound_val(
4879 __isl_take isl_basic_set *bset,
4880 enum isl_dim_type type, unsigned pos,
4881 __isl_take isl_val *value);
4882 __isl_give isl_set *isl_set_lower_bound_si(
4883 __isl_take isl_set *set,
4884 enum isl_dim_type type, unsigned pos, int value);
4885 __isl_give isl_set *isl_set_lower_bound_val(
4886 __isl_take isl_set *set,
4887 enum isl_dim_type type, unsigned pos,
4888 __isl_take isl_val *value);
4889 __isl_give isl_set *isl_set_upper_bound_si(
4890 __isl_take isl_set *set,
4891 enum isl_dim_type type, unsigned pos, int value);
4892 __isl_give isl_set *isl_set_upper_bound_val(
4893 __isl_take isl_set *set,
4894 enum isl_dim_type type, unsigned pos,
4895 __isl_take isl_val *value);
4897 #include <isl/map.h>
4898 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4899 __isl_take isl_basic_map *bmap,
4900 enum isl_dim_type type, unsigned pos, int value);
4901 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4902 __isl_take isl_basic_map *bmap,
4903 enum isl_dim_type type, unsigned pos, int value);
4904 __isl_give isl_map *isl_map_lower_bound_si(
4905 __isl_take isl_map *map,
4906 enum isl_dim_type type, unsigned pos, int value);
4907 __isl_give isl_map *isl_map_upper_bound_si(
4908 __isl_take isl_map *map,
4909 enum isl_dim_type type, unsigned pos, int value);
4911 Intersect the set or relation with the half-space where the given
4912 dimension has a value bounded by the fixed given integer value.
4914 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4915 enum isl_dim_type type1, int pos1,
4916 enum isl_dim_type type2, int pos2);
4917 __isl_give isl_basic_map *isl_basic_map_equate(
4918 __isl_take isl_basic_map *bmap,
4919 enum isl_dim_type type1, int pos1,
4920 enum isl_dim_type type2, int pos2);
4921 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4922 enum isl_dim_type type1, int pos1,
4923 enum isl_dim_type type2, int pos2);
4925 Intersect the set or relation with the hyperplane where the given
4926 dimensions are equal to each other.
4928 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4929 enum isl_dim_type type1, int pos1,
4930 enum isl_dim_type type2, int pos2);
4932 Intersect the relation with the hyperplane where the given
4933 dimensions have opposite values.
4935 __isl_give isl_map *isl_map_order_le(
4936 __isl_take isl_map *map,
4937 enum isl_dim_type type1, int pos1,
4938 enum isl_dim_type type2, int pos2);
4939 __isl_give isl_basic_map *isl_basic_map_order_ge(
4940 __isl_take isl_basic_map *bmap,
4941 enum isl_dim_type type1, int pos1,
4942 enum isl_dim_type type2, int pos2);
4943 __isl_give isl_map *isl_map_order_ge(
4944 __isl_take isl_map *map,
4945 enum isl_dim_type type1, int pos1,
4946 enum isl_dim_type type2, int pos2);
4947 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4948 enum isl_dim_type type1, int pos1,
4949 enum isl_dim_type type2, int pos2);
4950 __isl_give isl_basic_map *isl_basic_map_order_gt(
4951 __isl_take isl_basic_map *bmap,
4952 enum isl_dim_type type1, int pos1,
4953 enum isl_dim_type type2, int pos2);
4954 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4955 enum isl_dim_type type1, int pos1,
4956 enum isl_dim_type type2, int pos2);
4958 Intersect the relation with the half-space where the given
4959 dimensions satisfy the given ordering.
4961 #include <isl/union_set.h>
4962 __isl_give isl_union_map *isl_union_map_remove_map_if(
4963 __isl_take isl_union_map *umap,
4964 isl_bool (*fn)(__isl_keep isl_map *map,
4965 void *user), void *user);
4967 This function calls the callback function once for each
4968 pair of spaces for which there are elements in the input.
4969 If the callback returns C<isl_bool_true>, then all those elements
4970 are removed from the result. The only remaining elements in the output
4971 are then those for which the callback returns C<isl_bool_false>.
4975 #include <isl/aff.h>
4976 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4977 __isl_take isl_aff *aff);
4978 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4979 __isl_take isl_aff *aff);
4980 __isl_give isl_set *isl_pw_aff_pos_set(
4981 __isl_take isl_pw_aff *pa);
4982 __isl_give isl_set *isl_pw_aff_nonneg_set(
4983 __isl_take isl_pw_aff *pwaff);
4984 __isl_give isl_set *isl_pw_aff_zero_set(
4985 __isl_take isl_pw_aff *pwaff);
4986 __isl_give isl_set *isl_pw_aff_non_zero_set(
4987 __isl_take isl_pw_aff *pwaff);
4988 __isl_give isl_union_set *
4989 isl_union_pw_aff_zero_union_set(
4990 __isl_take isl_union_pw_aff *upa);
4991 __isl_give isl_union_set *
4992 isl_multi_union_pw_aff_zero_union_set(
4993 __isl_take isl_multi_union_pw_aff *mupa);
4995 The function C<isl_aff_neg_basic_set> returns a basic set
4996 containing those elements in the domain space
4997 of C<aff> where C<aff> is negative.
4998 The function C<isl_pw_aff_nonneg_set> returns a set
4999 containing those elements in the domain
5000 of C<pwaff> where C<pwaff> is non-negative.
5001 The function C<isl_multi_union_pw_aff_zero_union_set>
5002 returns a union set containing those elements
5003 in the domains of its elements where they are all zero.
5007 __isl_give isl_map *isl_set_identity(
5008 __isl_take isl_set *set);
5009 __isl_give isl_union_map *isl_union_set_identity(
5010 __isl_take isl_union_set *uset);
5011 __isl_give isl_union_pw_multi_aff *
5012 isl_union_set_identity_union_pw_multi_aff(
5013 __isl_take isl_union_set *uset);
5015 Construct an identity relation on the given (union) set.
5017 =item * Function Extraction
5019 A piecewise quasi affine expression that is equal to 1 on a set
5020 and 0 outside the set can be created using the following function.
5022 #include <isl/aff.h>
5023 __isl_give isl_pw_aff *isl_set_indicator_function(
5024 __isl_take isl_set *set);
5026 A piecewise multiple quasi affine expression can be extracted
5027 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
5028 and the C<isl_map> is single-valued.
5029 In case of a conversion from an C<isl_union_map>
5030 to an C<isl_union_pw_multi_aff>, these properties need to hold
5031 in each domain space.
5032 A conversion to a C<isl_multi_union_pw_aff> additionally
5033 requires that the input is non-empty and involves only a single
5036 #include <isl/aff.h>
5037 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
5038 __isl_take isl_set *set);
5039 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
5040 __isl_take isl_map *map);
5042 __isl_give isl_union_pw_multi_aff *
5043 isl_union_pw_multi_aff_from_union_set(
5044 __isl_take isl_union_set *uset);
5045 __isl_give isl_union_pw_multi_aff *
5046 isl_union_pw_multi_aff_from_union_map(
5047 __isl_take isl_union_map *umap);
5049 __isl_give isl_multi_union_pw_aff *
5050 isl_multi_union_pw_aff_from_union_map(
5051 __isl_take isl_union_map *umap);
5055 __isl_give isl_basic_set *isl_basic_map_deltas(
5056 __isl_take isl_basic_map *bmap);
5057 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
5058 __isl_give isl_union_set *isl_union_map_deltas(
5059 __isl_take isl_union_map *umap);
5061 These functions return a (basic) set containing the differences
5062 between image elements and corresponding domain elements in the input.
5064 __isl_give isl_basic_map *isl_basic_map_deltas_map(
5065 __isl_take isl_basic_map *bmap);
5066 __isl_give isl_map *isl_map_deltas_map(
5067 __isl_take isl_map *map);
5068 __isl_give isl_union_map *isl_union_map_deltas_map(
5069 __isl_take isl_union_map *umap);
5071 The functions above construct a (basic, regular or union) relation
5072 that maps (a wrapped version of) the input relation to its delta set.
5076 Simplify the representation of a set, relation or functions by trying
5077 to combine pairs of basic sets or relations into a single
5078 basic set or relation.
5080 #include <isl/set.h>
5081 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
5083 #include <isl/map.h>
5084 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5086 #include <isl/union_set.h>
5087 __isl_give isl_union_set *isl_union_set_coalesce(
5088 __isl_take isl_union_set *uset);
5090 #include <isl/union_map.h>
5091 __isl_give isl_union_map *isl_union_map_coalesce(
5092 __isl_take isl_union_map *umap);
5094 #include <isl/aff.h>
5095 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5096 __isl_take isl_pw_aff *pwqp);
5097 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5098 __isl_take isl_pw_multi_aff *pma);
5099 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5100 __isl_take isl_multi_pw_aff *mpa);
5101 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5102 __isl_take isl_union_pw_aff *upa);
5103 __isl_give isl_union_pw_multi_aff *
5104 isl_union_pw_multi_aff_coalesce(
5105 __isl_take isl_union_pw_multi_aff *upma);
5106 __isl_give isl_multi_union_pw_aff *
5107 isl_multi_union_pw_aff_coalesce(
5108 __isl_take isl_multi_union_pw_aff *aff);
5110 #include <isl/polynomial.h>
5111 __isl_give isl_pw_qpolynomial_fold *
5112 isl_pw_qpolynomial_fold_coalesce(
5113 __isl_take isl_pw_qpolynomial_fold *pwf);
5114 __isl_give isl_union_pw_qpolynomial *
5115 isl_union_pw_qpolynomial_coalesce(
5116 __isl_take isl_union_pw_qpolynomial *upwqp);
5117 __isl_give isl_union_pw_qpolynomial_fold *
5118 isl_union_pw_qpolynomial_fold_coalesce(
5119 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5121 One of the methods for combining pairs of basic sets or relations
5122 can result in coefficients that are much larger than those that appear
5123 in the constraints of the input. By default, the coefficients are
5124 not allowed to grow larger, but this can be changed by unsetting
5125 the following option.
5127 isl_stat isl_options_set_coalesce_bounded_wrapping(
5128 isl_ctx *ctx, int val);
5129 int isl_options_get_coalesce_bounded_wrapping(
5132 =item * Detecting equalities
5134 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5135 __isl_take isl_basic_set *bset);
5136 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5137 __isl_take isl_basic_map *bmap);
5138 __isl_give isl_set *isl_set_detect_equalities(
5139 __isl_take isl_set *set);
5140 __isl_give isl_map *isl_map_detect_equalities(
5141 __isl_take isl_map *map);
5142 __isl_give isl_union_set *isl_union_set_detect_equalities(
5143 __isl_take isl_union_set *uset);
5144 __isl_give isl_union_map *isl_union_map_detect_equalities(
5145 __isl_take isl_union_map *umap);
5147 Simplify the representation of a set or relation by detecting implicit
5150 =item * Removing redundant constraints
5152 #include <isl/set.h>
5153 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5154 __isl_take isl_basic_set *bset);
5155 __isl_give isl_set *isl_set_remove_redundancies(
5156 __isl_take isl_set *set);
5158 #include <isl/union_set.h>
5159 __isl_give isl_union_set *
5160 isl_union_set_remove_redundancies(
5161 __isl_take isl_union_set *uset);
5163 #include <isl/map.h>
5164 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5165 __isl_take isl_basic_map *bmap);
5166 __isl_give isl_map *isl_map_remove_redundancies(
5167 __isl_take isl_map *map);
5169 #include <isl/union_map.h>
5170 __isl_give isl_union_map *
5171 isl_union_map_remove_redundancies(
5172 __isl_take isl_union_map *umap);
5176 __isl_give isl_basic_set *isl_set_convex_hull(
5177 __isl_take isl_set *set);
5178 __isl_give isl_basic_map *isl_map_convex_hull(
5179 __isl_take isl_map *map);
5181 If the input set or relation has any existentially quantified
5182 variables, then the result of these operations is currently undefined.
5186 #include <isl/set.h>
5187 __isl_give isl_basic_set *
5188 isl_set_unshifted_simple_hull(
5189 __isl_take isl_set *set);
5190 __isl_give isl_basic_set *isl_set_simple_hull(
5191 __isl_take isl_set *set);
5192 __isl_give isl_basic_set *
5193 isl_set_plain_unshifted_simple_hull(
5194 __isl_take isl_set *set);
5195 __isl_give isl_basic_set *
5196 isl_set_unshifted_simple_hull_from_set_list(
5197 __isl_take isl_set *set,
5198 __isl_take isl_set_list *list);
5200 #include <isl/map.h>
5201 __isl_give isl_basic_map *
5202 isl_map_unshifted_simple_hull(
5203 __isl_take isl_map *map);
5204 __isl_give isl_basic_map *isl_map_simple_hull(
5205 __isl_take isl_map *map);
5206 __isl_give isl_basic_map *
5207 isl_map_plain_unshifted_simple_hull(
5208 __isl_take isl_map *map);
5209 __isl_give isl_basic_map *
5210 isl_map_unshifted_simple_hull_from_map_list(
5211 __isl_take isl_map *map,
5212 __isl_take isl_map_list *list);
5214 #include <isl/union_map.h>
5215 __isl_give isl_union_map *isl_union_map_simple_hull(
5216 __isl_take isl_union_map *umap);
5218 These functions compute a single basic set or relation
5219 that contains the whole input set or relation.
5220 In particular, the output is described by translates
5221 of the constraints describing the basic sets or relations in the input.
5222 In case of C<isl_set_unshifted_simple_hull>, only the original
5223 constraints are used, without any translation.
5224 In case of C<isl_set_plain_unshifted_simple_hull> and
5225 C<isl_map_plain_unshifted_simple_hull>, the result is described
5226 by original constraints that are obviously satisfied
5227 by the entire input set or relation.
5228 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5229 C<isl_map_unshifted_simple_hull_from_map_list>, the
5230 constraints are taken from the elements of the second argument.
5234 (See \autoref{s:simple hull}.)
5240 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5241 __isl_take isl_basic_set *bset);
5242 __isl_give isl_basic_set *isl_set_affine_hull(
5243 __isl_take isl_set *set);
5244 __isl_give isl_union_set *isl_union_set_affine_hull(
5245 __isl_take isl_union_set *uset);
5246 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5247 __isl_take isl_basic_map *bmap);
5248 __isl_give isl_basic_map *isl_map_affine_hull(
5249 __isl_take isl_map *map);
5250 __isl_give isl_union_map *isl_union_map_affine_hull(
5251 __isl_take isl_union_map *umap);
5253 In case of union sets and relations, the affine hull is computed
5256 =item * Polyhedral hull
5258 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5259 __isl_take isl_set *set);
5260 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5261 __isl_take isl_map *map);
5262 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5263 __isl_take isl_union_set *uset);
5264 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5265 __isl_take isl_union_map *umap);
5267 These functions compute a single basic set or relation
5268 not involving any existentially quantified variables
5269 that contains the whole input set or relation.
5270 In case of union sets and relations, the polyhedral hull is computed
5275 #include <isl/map.h>
5276 __isl_give isl_fixed_box *
5277 isl_map_get_range_simple_fixed_box_hull(
5278 __isl_keep isl_map *map);
5280 This function tries to approximate the range of the map by a box of fixed size.
5281 The box is described in terms of an offset living in the same space as
5282 the input map and a size living in the range space. For any element
5283 in the input map, the range value is greater than or equal to
5284 the offset applied to the domain value and the difference with
5285 this offset is strictly smaller than the size.
5286 If no fixed-size approximation of the range can be found,
5287 an I<invalid> box is returned, i.e., one for which
5288 C<isl_fixed_box_is_valid> below returns false.
5290 The validity, the offset and the size of the box can be obtained using
5291 the following functions.
5293 #include <isl/fixed_box.h>
5294 isl_bool isl_fixed_box_is_valid(
5295 __isl_keep isl_fixed_box *box);
5296 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
5297 __isl_keep isl_fixed_box *box);
5298 __isl_give isl_multi_val *isl_fixed_box_get_size(
5299 __isl_keep isl_fixed_box *box);
5301 The box can be copied and freed using the following functions.
5303 #include <isl/fixed_box.h>
5304 __isl_give isl_fixed_box *isl_fixed_box_copy(
5305 __isl_keep isl_fixed_box *box);
5306 __isl_null isl_fixed_box *isl_fixed_box_free(
5307 __isl_take isl_fixed_box *box);
5309 =item * Other approximations
5311 #include <isl/set.h>
5312 __isl_give isl_basic_set *
5313 isl_basic_set_drop_constraints_involving_dims(
5314 __isl_take isl_basic_set *bset,
5315 enum isl_dim_type type,
5316 unsigned first, unsigned n);
5317 __isl_give isl_basic_set *
5318 isl_basic_set_drop_constraints_not_involving_dims(
5319 __isl_take isl_basic_set *bset,
5320 enum isl_dim_type type,
5321 unsigned first, unsigned n);
5322 __isl_give isl_set *
5323 isl_set_drop_constraints_involving_dims(
5324 __isl_take isl_set *set,
5325 enum isl_dim_type type,
5326 unsigned first, unsigned n);
5327 __isl_give isl_set *
5328 isl_set_drop_constraints_not_involving_dims(
5329 __isl_take isl_set *set,
5330 enum isl_dim_type type,
5331 unsigned first, unsigned n);
5333 #include <isl/map.h>
5334 __isl_give isl_basic_map *
5335 isl_basic_map_drop_constraints_involving_dims(
5336 __isl_take isl_basic_map *bmap,
5337 enum isl_dim_type type,
5338 unsigned first, unsigned n);
5339 __isl_give isl_basic_map *
5340 isl_basic_map_drop_constraints_not_involving_dims(
5341 __isl_take isl_basic_map *bmap,
5342 enum isl_dim_type type,
5343 unsigned first, unsigned n);
5344 __isl_give isl_map *
5345 isl_map_drop_constraints_involving_dims(
5346 __isl_take isl_map *map,
5347 enum isl_dim_type type,
5348 unsigned first, unsigned n);
5349 __isl_give isl_map *
5350 isl_map_drop_constraints_not_involving_dims(
5351 __isl_take isl_map *map,
5352 enum isl_dim_type type,
5353 unsigned first, unsigned n);
5355 These functions drop any constraints (not) involving the specified dimensions.
5356 Note that the result depends on the representation of the input.
5358 #include <isl/polynomial.h>
5359 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5360 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5361 __isl_give isl_union_pw_qpolynomial *
5362 isl_union_pw_qpolynomial_to_polynomial(
5363 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5365 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5366 the polynomial will be an overapproximation. If C<sign> is negative,
5367 it will be an underapproximation. If C<sign> is zero, the approximation
5368 will lie somewhere in between.
5372 __isl_give isl_basic_set *isl_basic_set_sample(
5373 __isl_take isl_basic_set *bset);
5374 __isl_give isl_basic_set *isl_set_sample(
5375 __isl_take isl_set *set);
5376 __isl_give isl_basic_map *isl_basic_map_sample(
5377 __isl_take isl_basic_map *bmap);
5378 __isl_give isl_basic_map *isl_map_sample(
5379 __isl_take isl_map *map);
5381 If the input (basic) set or relation is non-empty, then return
5382 a singleton subset of the input. Otherwise, return an empty set.
5384 =item * Optimization
5386 #include <isl/ilp.h>
5387 __isl_give isl_val *isl_basic_set_max_val(
5388 __isl_keep isl_basic_set *bset,
5389 __isl_keep isl_aff *obj);
5390 __isl_give isl_val *isl_set_min_val(
5391 __isl_keep isl_set *set,
5392 __isl_keep isl_aff *obj);
5393 __isl_give isl_val *isl_set_max_val(
5394 __isl_keep isl_set *set,
5395 __isl_keep isl_aff *obj);
5396 __isl_give isl_multi_val *
5397 isl_union_set_min_multi_union_pw_aff(
5398 __isl_keep isl_union_set *uset,
5399 __isl_keep isl_multi_union_pw_aff *obj);
5401 Compute the minimum or maximum of the integer affine expression C<obj>
5402 over the points in C<set>.
5403 The result is C<NULL> in case of an error, the optimal value in case
5404 there is one, negative infinity or infinity if the problem is unbounded and
5405 NaN if the problem is empty.
5407 #include <isl/ilp.h>
5408 __isl_give isl_val *isl_union_pw_aff_min_val(
5409 __isl_take isl_union_pw_aff *upa);
5410 __isl_give isl_val *isl_union_pw_aff_max_val(
5411 __isl_take isl_union_pw_aff *upa);
5412 __isl_give isl_multi_val *
5413 isl_multi_union_pw_aff_min_multi_val(
5414 __isl_take isl_multi_union_pw_aff *mupa);
5415 __isl_give isl_multi_val *
5416 isl_multi_union_pw_aff_max_multi_val(
5417 __isl_take isl_multi_union_pw_aff *mupa);
5419 Compute the minimum or maximum of the integer affine expression
5420 over its definition domain.
5421 The result is C<NULL> in case of an error, the optimal value in case
5422 there is one, negative infinity or infinity if the problem is unbounded and
5423 NaN if the problem is empty.
5425 #include <isl/ilp.h>
5426 __isl_give isl_val *isl_basic_set_dim_max_val(
5427 __isl_take isl_basic_set *bset, int pos);
5429 Return the maximal value attained by the given set dimension,
5430 independently of the parameter values and of any other dimensions.
5431 The result is C<NULL> in case of an error, the optimal value in case
5432 there is one, infinity if the problem is unbounded and
5433 NaN if the input is empty.
5435 =item * Parametric optimization
5437 __isl_give isl_pw_aff *isl_set_dim_min(
5438 __isl_take isl_set *set, int pos);
5439 __isl_give isl_pw_aff *isl_set_dim_max(
5440 __isl_take isl_set *set, int pos);
5441 __isl_give isl_pw_aff *isl_map_dim_min(
5442 __isl_take isl_map *map, int pos);
5443 __isl_give isl_pw_aff *isl_map_dim_max(
5444 __isl_take isl_map *map, int pos);
5446 Compute the minimum or maximum of the given set or output dimension
5447 as a function of the parameters (and input dimensions), but independently
5448 of the other set or output dimensions.
5449 For lexicographic optimization, see L<"Lexicographic Optimization">.
5453 The following functions compute either the set of (rational) coefficient
5454 values of valid constraints for the given set or the set of (rational)
5455 values satisfying the constraints with coefficients from the given set.
5456 Internally, these two sets of functions perform essentially the
5457 same operations, except that the set of coefficients is assumed to
5458 be a cone, while the set of values may be any polyhedron.
5459 The current implementation is based on the Farkas lemma and
5460 Fourier-Motzkin elimination, but this may change or be made optional
5461 in future. In particular, future implementations may use different
5462 dualization algorithms or skip the elimination step.
5464 #include <isl/set.h>
5465 __isl_give isl_basic_set *isl_basic_set_coefficients(
5466 __isl_take isl_basic_set *bset);
5467 __isl_give isl_basic_set_list *
5468 isl_basic_set_list_coefficients(
5469 __isl_take isl_basic_set_list *list);
5470 __isl_give isl_basic_set *isl_set_coefficients(
5471 __isl_take isl_set *set);
5472 __isl_give isl_union_set *isl_union_set_coefficients(
5473 __isl_take isl_union_set *bset);
5474 __isl_give isl_basic_set *isl_basic_set_solutions(
5475 __isl_take isl_basic_set *bset);
5476 __isl_give isl_basic_set *isl_set_solutions(
5477 __isl_take isl_set *set);
5478 __isl_give isl_union_set *isl_union_set_solutions(
5479 __isl_take isl_union_set *bset);
5483 __isl_give isl_map *isl_map_fixed_power_val(
5484 __isl_take isl_map *map,
5485 __isl_take isl_val *exp);
5486 __isl_give isl_union_map *
5487 isl_union_map_fixed_power_val(
5488 __isl_take isl_union_map *umap,
5489 __isl_take isl_val *exp);
5491 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5492 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5493 of C<map> is computed.
5495 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5497 __isl_give isl_union_map *isl_union_map_power(
5498 __isl_take isl_union_map *umap, int *exact);
5500 Compute a parametric representation for all positive powers I<k> of C<map>.
5501 The result maps I<k> to a nested relation corresponding to the
5502 I<k>th power of C<map>.
5503 The result may be an overapproximation. If the result is known to be exact,
5504 then C<*exact> is set to C<1>.
5506 =item * Transitive closure
5508 __isl_give isl_map *isl_map_transitive_closure(
5509 __isl_take isl_map *map, int *exact);
5510 __isl_give isl_union_map *isl_union_map_transitive_closure(
5511 __isl_take isl_union_map *umap, int *exact);
5513 Compute the transitive closure of C<map>.
5514 The result may be an overapproximation. If the result is known to be exact,
5515 then C<*exact> is set to C<1>.
5517 =item * Reaching path lengths
5519 __isl_give isl_map *isl_map_reaching_path_lengths(
5520 __isl_take isl_map *map, int *exact);
5522 Compute a relation that maps each element in the range of C<map>
5523 to the lengths of all paths composed of edges in C<map> that
5524 end up in the given element.
5525 The result may be an overapproximation. If the result is known to be exact,
5526 then C<*exact> is set to C<1>.
5527 To compute the I<maximal> path length, the resulting relation
5528 should be postprocessed by C<isl_map_lexmax>.
5529 In particular, if the input relation is a dependence relation
5530 (mapping sources to sinks), then the maximal path length corresponds
5531 to the free schedule.
5532 Note, however, that C<isl_map_lexmax> expects the maximum to be
5533 finite, so if the path lengths are unbounded (possibly due to
5534 the overapproximation), then you will get an error message.
5538 #include <isl/space.h>
5539 __isl_give isl_space *isl_space_wrap(
5540 __isl_take isl_space *space);
5541 __isl_give isl_space *isl_space_unwrap(
5542 __isl_take isl_space *space);
5544 #include <isl/local_space.h>
5545 __isl_give isl_local_space *isl_local_space_wrap(
5546 __isl_take isl_local_space *ls);
5548 #include <isl/set.h>
5549 __isl_give isl_basic_map *isl_basic_set_unwrap(
5550 __isl_take isl_basic_set *bset);
5551 __isl_give isl_map *isl_set_unwrap(
5552 __isl_take isl_set *set);
5554 #include <isl/map.h>
5555 __isl_give isl_basic_set *isl_basic_map_wrap(
5556 __isl_take isl_basic_map *bmap);
5557 __isl_give isl_set *isl_map_wrap(
5558 __isl_take isl_map *map);
5560 #include <isl/union_set.h>
5561 __isl_give isl_union_map *isl_union_set_unwrap(
5562 __isl_take isl_union_set *uset);
5564 #include <isl/union_map.h>
5565 __isl_give isl_union_set *isl_union_map_wrap(
5566 __isl_take isl_union_map *umap);
5568 The input to C<isl_space_unwrap> should
5569 be the space of a set, while that of
5570 C<isl_space_wrap> should be the space of a relation.
5571 Conversely, the output of C<isl_space_unwrap> is the space
5572 of a relation, while that of C<isl_space_wrap> is the space of a set.
5576 Remove any internal structure of domain (and range) of the given
5577 set or relation. If there is any such internal structure in the input,
5578 then the name of the space is also removed.
5580 #include <isl/space.h>
5581 __isl_give isl_space *isl_space_flatten_domain(
5582 __isl_take isl_space *space);
5583 __isl_give isl_space *isl_space_flatten_range(
5584 __isl_take isl_space *space);
5586 #include <isl/local_space.h>
5587 __isl_give isl_local_space *
5588 isl_local_space_flatten_domain(
5589 __isl_take isl_local_space *ls);
5590 __isl_give isl_local_space *
5591 isl_local_space_flatten_range(
5592 __isl_take isl_local_space *ls);
5594 #include <isl/set.h>
5595 __isl_give isl_basic_set *isl_basic_set_flatten(
5596 __isl_take isl_basic_set *bset);
5597 __isl_give isl_set *isl_set_flatten(
5598 __isl_take isl_set *set);
5600 #include <isl/map.h>
5601 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5602 __isl_take isl_basic_map *bmap);
5603 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5604 __isl_take isl_basic_map *bmap);
5605 __isl_give isl_map *isl_map_flatten_range(
5606 __isl_take isl_map *map);
5607 __isl_give isl_map *isl_map_flatten_domain(
5608 __isl_take isl_map *map);
5609 __isl_give isl_basic_map *isl_basic_map_flatten(
5610 __isl_take isl_basic_map *bmap);
5611 __isl_give isl_map *isl_map_flatten(
5612 __isl_take isl_map *map);
5614 #include <isl/val.h>
5615 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5616 __isl_take isl_multi_val *mv);
5618 #include <isl/aff.h>
5619 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5620 __isl_take isl_multi_aff *ma);
5621 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5622 __isl_take isl_multi_aff *ma);
5623 __isl_give isl_multi_pw_aff *
5624 isl_multi_pw_aff_flatten_range(
5625 __isl_take isl_multi_pw_aff *mpa);
5626 __isl_give isl_multi_union_pw_aff *
5627 isl_multi_union_pw_aff_flatten_range(
5628 __isl_take isl_multi_union_pw_aff *mupa);
5630 #include <isl/map.h>
5631 __isl_give isl_map *isl_set_flatten_map(
5632 __isl_take isl_set *set);
5634 The function above constructs a relation
5635 that maps the input set to a flattened version of the set.
5639 Lift the input set to a space with extra dimensions corresponding
5640 to the existentially quantified variables in the input.
5641 In particular, the result lives in a wrapped map where the domain
5642 is the original space and the range corresponds to the original
5643 existentially quantified variables.
5645 #include <isl/set.h>
5646 __isl_give isl_basic_set *isl_basic_set_lift(
5647 __isl_take isl_basic_set *bset);
5648 __isl_give isl_set *isl_set_lift(
5649 __isl_take isl_set *set);
5650 __isl_give isl_union_set *isl_union_set_lift(
5651 __isl_take isl_union_set *uset);
5653 Given a local space that contains the existentially quantified
5654 variables of a set, a basic relation that, when applied to
5655 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5656 can be constructed using the following function.
5658 #include <isl/local_space.h>
5659 __isl_give isl_basic_map *isl_local_space_lifting(
5660 __isl_take isl_local_space *ls);
5662 #include <isl/aff.h>
5663 __isl_give isl_multi_aff *isl_multi_aff_lift(
5664 __isl_take isl_multi_aff *maff,
5665 __isl_give isl_local_space **ls);
5667 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5668 then it is assigned the local space that lies at the basis of
5669 the lifting applied.
5671 =item * Internal Product
5673 #include <isl/space.h>
5674 __isl_give isl_space *isl_space_zip(
5675 __isl_take isl_space *space);
5677 #include <isl/map.h>
5678 __isl_give isl_basic_map *isl_basic_map_zip(
5679 __isl_take isl_basic_map *bmap);
5680 __isl_give isl_map *isl_map_zip(
5681 __isl_take isl_map *map);
5683 #include <isl/union_map.h>
5684 __isl_give isl_union_map *isl_union_map_zip(
5685 __isl_take isl_union_map *umap);
5687 Given a relation with nested relations for domain and range,
5688 interchange the range of the domain with the domain of the range.
5692 #include <isl/space.h>
5693 __isl_give isl_space *isl_space_curry(
5694 __isl_take isl_space *space);
5695 __isl_give isl_space *isl_space_uncurry(
5696 __isl_take isl_space *space);
5698 #include <isl/map.h>
5699 __isl_give isl_basic_map *isl_basic_map_curry(
5700 __isl_take isl_basic_map *bmap);
5701 __isl_give isl_basic_map *isl_basic_map_uncurry(
5702 __isl_take isl_basic_map *bmap);
5703 __isl_give isl_map *isl_map_curry(
5704 __isl_take isl_map *map);
5705 __isl_give isl_map *isl_map_uncurry(
5706 __isl_take isl_map *map);
5708 #include <isl/union_map.h>
5709 __isl_give isl_union_map *isl_union_map_curry(
5710 __isl_take isl_union_map *umap);
5711 __isl_give isl_union_map *isl_union_map_uncurry(
5712 __isl_take isl_union_map *umap);
5714 Given a relation with a nested relation for domain,
5715 the C<curry> functions
5716 move the range of the nested relation out of the domain
5717 and use it as the domain of a nested relation in the range,
5718 with the original range as range of this nested relation.
5719 The C<uncurry> functions perform the inverse operation.
5721 #include <isl/space.h>
5722 __isl_give isl_space *isl_space_range_curry(
5723 __isl_take isl_space *space);
5725 #include <isl/map.h>
5726 __isl_give isl_map *isl_map_range_curry(
5727 __isl_take isl_map *map);
5729 #include <isl/union_map.h>
5730 __isl_give isl_union_map *isl_union_map_range_curry(
5731 __isl_take isl_union_map *umap);
5733 These functions apply the currying to the relation that
5734 is nested inside the range of the input.
5736 =item * Aligning parameters
5738 Change the order of the parameters of the given set, relation
5740 such that the first parameters match those of C<model>.
5741 This may involve the introduction of extra parameters.
5742 All parameters need to be named.
5744 #include <isl/space.h>
5745 __isl_give isl_space *isl_space_align_params(
5746 __isl_take isl_space *space1,
5747 __isl_take isl_space *space2)
5749 #include <isl/set.h>
5750 __isl_give isl_basic_set *isl_basic_set_align_params(
5751 __isl_take isl_basic_set *bset,
5752 __isl_take isl_space *model);
5753 __isl_give isl_set *isl_set_align_params(
5754 __isl_take isl_set *set,
5755 __isl_take isl_space *model);
5757 #include <isl/map.h>
5758 __isl_give isl_basic_map *isl_basic_map_align_params(
5759 __isl_take isl_basic_map *bmap,
5760 __isl_take isl_space *model);
5761 __isl_give isl_map *isl_map_align_params(
5762 __isl_take isl_map *map,
5763 __isl_take isl_space *model);
5765 #include <isl/val.h>
5766 __isl_give isl_multi_val *isl_multi_val_align_params(
5767 __isl_take isl_multi_val *mv,
5768 __isl_take isl_space *model);
5770 #include <isl/aff.h>
5771 __isl_give isl_aff *isl_aff_align_params(
5772 __isl_take isl_aff *aff,
5773 __isl_take isl_space *model);
5774 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5775 __isl_take isl_multi_aff *multi,
5776 __isl_take isl_space *model);
5777 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5778 __isl_take isl_pw_aff *pwaff,
5779 __isl_take isl_space *model);
5780 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5781 __isl_take isl_pw_multi_aff *pma,
5782 __isl_take isl_space *model);
5783 __isl_give isl_union_pw_aff *
5784 isl_union_pw_aff_align_params(
5785 __isl_take isl_union_pw_aff *upa,
5786 __isl_take isl_space *model);
5787 __isl_give isl_union_pw_multi_aff *
5788 isl_union_pw_multi_aff_align_params(
5789 __isl_take isl_union_pw_multi_aff *upma,
5790 __isl_take isl_space *model);
5791 __isl_give isl_multi_union_pw_aff *
5792 isl_multi_union_pw_aff_align_params(
5793 __isl_take isl_multi_union_pw_aff *mupa,
5794 __isl_take isl_space *model);
5796 #include <isl/polynomial.h>
5797 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5798 __isl_take isl_qpolynomial *qp,
5799 __isl_take isl_space *model);
5801 =item * Drop unused parameters
5803 Drop parameters that are not referenced by the isl object.
5804 All parameters need to be named.
5806 #include <isl/set.h>
5807 __isl_give isl_basic_set *
5808 isl_basic_set_drop_unused_params(
5809 __isl_take isl_basic_set *bset);
5810 __isl_give isl_set *isl_set_drop_unused_params(
5811 __isl_take isl_set *set);
5813 #include <isl/map.h>
5814 __isl_give isl_basic_map *
5815 isl_basic_map_drop_unused_params(
5816 __isl_take isl_basic_map *bmap);
5817 __isl_give isl_map *isl_map_drop_unused_params(
5818 __isl_take isl_map *map);
5820 #include <isl/aff.h>
5821 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
5822 __isl_take isl_pw_aff *pa);
5823 __isl_give isl_pw_multi_aff *
5824 isl_pw_multi_aff_drop_unused_params(
5825 __isl_take isl_pw_multi_aff *pma);
5827 #include <isl/polynomial.h>
5828 __isl_give isl_pw_qpolynomial *
5829 isl_pw_qpolynomial_drop_unused_params(
5830 __isl_take isl_pw_qpolynomial *pwqp);
5831 __isl_give isl_pw_qpolynomial_fold *
5832 isl_pw_qpolynomial_fold_drop_unused_params(
5833 __isl_take isl_pw_qpolynomial_fold *pwf);
5835 =item * Unary Arithmetic Operations
5837 #include <isl/set.h>
5838 __isl_give isl_set *isl_set_neg(
5839 __isl_take isl_set *set);
5840 #include <isl/map.h>
5841 __isl_give isl_map *isl_map_neg(
5842 __isl_take isl_map *map);
5844 C<isl_set_neg> constructs a set containing the opposites of
5845 the elements in its argument.
5846 The domain of the result of C<isl_map_neg> is the same
5847 as the domain of its argument. The corresponding range
5848 elements are the opposites of the corresponding range
5849 elements in the argument.
5851 #include <isl/val.h>
5852 __isl_give isl_multi_val *isl_multi_val_neg(
5853 __isl_take isl_multi_val *mv);
5855 #include <isl/aff.h>
5856 __isl_give isl_aff *isl_aff_neg(
5857 __isl_take isl_aff *aff);
5858 __isl_give isl_multi_aff *isl_multi_aff_neg(
5859 __isl_take isl_multi_aff *ma);
5860 __isl_give isl_pw_aff *isl_pw_aff_neg(
5861 __isl_take isl_pw_aff *pwaff);
5862 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5863 __isl_take isl_pw_multi_aff *pma);
5864 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5865 __isl_take isl_multi_pw_aff *mpa);
5866 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5867 __isl_take isl_union_pw_aff *upa);
5868 __isl_give isl_union_pw_multi_aff *
5869 isl_union_pw_multi_aff_neg(
5870 __isl_take isl_union_pw_multi_aff *upma);
5871 __isl_give isl_multi_union_pw_aff *
5872 isl_multi_union_pw_aff_neg(
5873 __isl_take isl_multi_union_pw_aff *mupa);
5874 __isl_give isl_aff *isl_aff_ceil(
5875 __isl_take isl_aff *aff);
5876 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5877 __isl_take isl_pw_aff *pwaff);
5878 __isl_give isl_aff *isl_aff_floor(
5879 __isl_take isl_aff *aff);
5880 __isl_give isl_multi_aff *isl_multi_aff_floor(
5881 __isl_take isl_multi_aff *ma);
5882 __isl_give isl_pw_aff *isl_pw_aff_floor(
5883 __isl_take isl_pw_aff *pwaff);
5884 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5885 __isl_take isl_union_pw_aff *upa);
5886 __isl_give isl_multi_union_pw_aff *
5887 isl_multi_union_pw_aff_floor(
5888 __isl_take isl_multi_union_pw_aff *mupa);
5890 #include <isl/aff.h>
5891 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5892 __isl_take isl_pw_aff_list *list);
5893 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5894 __isl_take isl_pw_aff_list *list);
5896 #include <isl/polynomial.h>
5897 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5898 __isl_take isl_qpolynomial *qp);
5899 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5900 __isl_take isl_pw_qpolynomial *pwqp);
5901 __isl_give isl_union_pw_qpolynomial *
5902 isl_union_pw_qpolynomial_neg(
5903 __isl_take isl_union_pw_qpolynomial *upwqp);
5904 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5905 __isl_take isl_qpolynomial *qp,
5907 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5908 __isl_take isl_pw_qpolynomial *pwqp,
5913 The following functions evaluate a function in a point.
5915 #include <isl/aff.h>
5916 __isl_give isl_val *isl_aff_eval(
5917 __isl_take isl_aff *aff,
5918 __isl_take isl_point *pnt);
5919 __isl_give isl_val *isl_pw_aff_eval(
5920 __isl_take isl_pw_aff *pa,
5921 __isl_take isl_point *pnt);
5923 #include <isl/polynomial.h>
5924 __isl_give isl_val *isl_pw_qpolynomial_eval(
5925 __isl_take isl_pw_qpolynomial *pwqp,
5926 __isl_take isl_point *pnt);
5927 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5928 __isl_take isl_pw_qpolynomial_fold *pwf,
5929 __isl_take isl_point *pnt);
5930 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5931 __isl_take isl_union_pw_qpolynomial *upwqp,
5932 __isl_take isl_point *pnt);
5933 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5934 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5935 __isl_take isl_point *pnt);
5937 These functions return NaN when evaluated at a void point.
5938 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
5939 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
5940 when the function is evaluated outside its explicit domain.
5942 =item * Dimension manipulation
5944 It is usually not advisable to directly change the (input or output)
5945 space of a set or a relation as this removes the name and the internal
5946 structure of the space. However, the functions below can be useful
5947 to add new parameters, assuming
5948 C<isl_set_align_params> and C<isl_map_align_params>
5951 #include <isl/space.h>
5952 __isl_give isl_space *isl_space_add_dims(
5953 __isl_take isl_space *space,
5954 enum isl_dim_type type, unsigned n);
5955 __isl_give isl_space *isl_space_insert_dims(
5956 __isl_take isl_space *space,
5957 enum isl_dim_type type, unsigned pos, unsigned n);
5958 __isl_give isl_space *isl_space_drop_dims(
5959 __isl_take isl_space *space,
5960 enum isl_dim_type type, unsigned first, unsigned n);
5961 __isl_give isl_space *isl_space_move_dims(
5962 __isl_take isl_space *space,
5963 enum isl_dim_type dst_type, unsigned dst_pos,
5964 enum isl_dim_type src_type, unsigned src_pos,
5967 #include <isl/local_space.h>
5968 __isl_give isl_local_space *isl_local_space_add_dims(
5969 __isl_take isl_local_space *ls,
5970 enum isl_dim_type type, unsigned n);
5971 __isl_give isl_local_space *isl_local_space_insert_dims(
5972 __isl_take isl_local_space *ls,
5973 enum isl_dim_type type, unsigned first, unsigned n);
5974 __isl_give isl_local_space *isl_local_space_drop_dims(
5975 __isl_take isl_local_space *ls,
5976 enum isl_dim_type type, unsigned first, unsigned n);
5978 #include <isl/set.h>
5979 __isl_give isl_basic_set *isl_basic_set_add_dims(
5980 __isl_take isl_basic_set *bset,
5981 enum isl_dim_type type, unsigned n);
5982 __isl_give isl_set *isl_set_add_dims(
5983 __isl_take isl_set *set,
5984 enum isl_dim_type type, unsigned n);
5985 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5986 __isl_take isl_basic_set *bset,
5987 enum isl_dim_type type, unsigned pos,
5989 __isl_give isl_set *isl_set_insert_dims(
5990 __isl_take isl_set *set,
5991 enum isl_dim_type type, unsigned pos, unsigned n);
5992 __isl_give isl_basic_set *isl_basic_set_move_dims(
5993 __isl_take isl_basic_set *bset,
5994 enum isl_dim_type dst_type, unsigned dst_pos,
5995 enum isl_dim_type src_type, unsigned src_pos,
5997 __isl_give isl_set *isl_set_move_dims(
5998 __isl_take isl_set *set,
5999 enum isl_dim_type dst_type, unsigned dst_pos,
6000 enum isl_dim_type src_type, unsigned src_pos,
6003 #include <isl/map.h>
6004 __isl_give isl_basic_map *isl_basic_map_add_dims(
6005 __isl_take isl_basic_map *bmap,
6006 enum isl_dim_type type, unsigned n);
6007 __isl_give isl_map *isl_map_add_dims(
6008 __isl_take isl_map *map,
6009 enum isl_dim_type type, unsigned n);
6010 __isl_give isl_basic_map *isl_basic_map_insert_dims(
6011 __isl_take isl_basic_map *bmap,
6012 enum isl_dim_type type, unsigned pos,
6014 __isl_give isl_map *isl_map_insert_dims(
6015 __isl_take isl_map *map,
6016 enum isl_dim_type type, unsigned pos, unsigned n);
6017 __isl_give isl_basic_map *isl_basic_map_move_dims(
6018 __isl_take isl_basic_map *bmap,
6019 enum isl_dim_type dst_type, unsigned dst_pos,
6020 enum isl_dim_type src_type, unsigned src_pos,
6022 __isl_give isl_map *isl_map_move_dims(
6023 __isl_take isl_map *map,
6024 enum isl_dim_type dst_type, unsigned dst_pos,
6025 enum isl_dim_type src_type, unsigned src_pos,
6028 #include <isl/val.h>
6029 __isl_give isl_multi_val *isl_multi_val_insert_dims(
6030 __isl_take isl_multi_val *mv,
6031 enum isl_dim_type type, unsigned first, unsigned n);
6032 __isl_give isl_multi_val *isl_multi_val_add_dims(
6033 __isl_take isl_multi_val *mv,
6034 enum isl_dim_type type, unsigned n);
6035 __isl_give isl_multi_val *isl_multi_val_drop_dims(
6036 __isl_take isl_multi_val *mv,
6037 enum isl_dim_type type, unsigned first, unsigned n);
6039 #include <isl/aff.h>
6040 __isl_give isl_aff *isl_aff_insert_dims(
6041 __isl_take isl_aff *aff,
6042 enum isl_dim_type type, unsigned first, unsigned n);
6043 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
6044 __isl_take isl_multi_aff *ma,
6045 enum isl_dim_type type, unsigned first, unsigned n);
6046 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
6047 __isl_take isl_pw_aff *pwaff,
6048 enum isl_dim_type type, unsigned first, unsigned n);
6049 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
6050 __isl_take isl_multi_pw_aff *mpa,
6051 enum isl_dim_type type, unsigned first, unsigned n);
6052 __isl_give isl_aff *isl_aff_add_dims(
6053 __isl_take isl_aff *aff,
6054 enum isl_dim_type type, unsigned n);
6055 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
6056 __isl_take isl_multi_aff *ma,
6057 enum isl_dim_type type, unsigned n);
6058 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
6059 __isl_take isl_pw_aff *pwaff,
6060 enum isl_dim_type type, unsigned n);
6061 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
6062 __isl_take isl_multi_pw_aff *mpa,
6063 enum isl_dim_type type, unsigned n);
6064 __isl_give isl_aff *isl_aff_drop_dims(
6065 __isl_take isl_aff *aff,
6066 enum isl_dim_type type, unsigned first, unsigned n);
6067 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
6068 __isl_take isl_multi_aff *maff,
6069 enum isl_dim_type type, unsigned first, unsigned n);
6070 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
6071 __isl_take isl_pw_aff *pwaff,
6072 enum isl_dim_type type, unsigned first, unsigned n);
6073 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
6074 __isl_take isl_pw_multi_aff *pma,
6075 enum isl_dim_type type, unsigned first, unsigned n);
6076 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
6077 __isl_take isl_union_pw_aff *upa,
6078 enum isl_dim_type type, unsigned first, unsigned n);
6079 __isl_give isl_union_pw_multi_aff *
6080 isl_union_pw_multi_aff_drop_dims(
6081 __isl_take isl_union_pw_multi_aff *upma,
6082 enum isl_dim_type type,
6083 unsigned first, unsigned n);
6084 __isl_give isl_multi_union_pw_aff *
6085 isl_multi_union_pw_aff_drop_dims(
6086 __isl_take isl_multi_union_pw_aff *mupa,
6087 enum isl_dim_type type, unsigned first,
6089 __isl_give isl_aff *isl_aff_move_dims(
6090 __isl_take isl_aff *aff,
6091 enum isl_dim_type dst_type, unsigned dst_pos,
6092 enum isl_dim_type src_type, unsigned src_pos,
6094 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
6095 __isl_take isl_multi_aff *ma,
6096 enum isl_dim_type dst_type, unsigned dst_pos,
6097 enum isl_dim_type src_type, unsigned src_pos,
6099 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
6100 __isl_take isl_pw_aff *pa,
6101 enum isl_dim_type dst_type, unsigned dst_pos,
6102 enum isl_dim_type src_type, unsigned src_pos,
6104 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
6105 __isl_take isl_multi_pw_aff *pma,
6106 enum isl_dim_type dst_type, unsigned dst_pos,
6107 enum isl_dim_type src_type, unsigned src_pos,
6110 #include <isl/polynomial.h>
6111 __isl_give isl_union_pw_qpolynomial *
6112 isl_union_pw_qpolynomial_drop_dims(
6113 __isl_take isl_union_pw_qpolynomial *upwqp,
6114 enum isl_dim_type type,
6115 unsigned first, unsigned n);
6116 __isl_give isl_union_pw_qpolynomial_fold *
6117 isl_union_pw_qpolynomial_fold_drop_dims(
6118 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6119 enum isl_dim_type type,
6120 unsigned first, unsigned n);
6122 The operations on union expressions can only manipulate parameters.
6126 =head2 Binary Operations
6128 The two arguments of a binary operation not only need to live
6129 in the same C<isl_ctx>, they currently also need to have
6130 the same (number of) parameters.
6132 =head3 Basic Operations
6136 =item * Intersection
6138 #include <isl/local_space.h>
6139 __isl_give isl_local_space *isl_local_space_intersect(
6140 __isl_take isl_local_space *ls1,
6141 __isl_take isl_local_space *ls2);
6143 #include <isl/set.h>
6144 __isl_give isl_basic_set *isl_basic_set_intersect_params(
6145 __isl_take isl_basic_set *bset1,
6146 __isl_take isl_basic_set *bset2);
6147 __isl_give isl_basic_set *isl_basic_set_intersect(
6148 __isl_take isl_basic_set *bset1,
6149 __isl_take isl_basic_set *bset2);
6150 __isl_give isl_basic_set *isl_basic_set_list_intersect(
6151 __isl_take struct isl_basic_set_list *list);
6152 __isl_give isl_set *isl_set_intersect_params(
6153 __isl_take isl_set *set,
6154 __isl_take isl_set *params);
6155 __isl_give isl_set *isl_set_intersect(
6156 __isl_take isl_set *set1,
6157 __isl_take isl_set *set2);
6159 #include <isl/map.h>
6160 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
6161 __isl_take isl_basic_map *bmap,
6162 __isl_take isl_basic_set *bset);
6163 __isl_give isl_basic_map *isl_basic_map_intersect_range(
6164 __isl_take isl_basic_map *bmap,
6165 __isl_take isl_basic_set *bset);
6166 __isl_give isl_basic_map *isl_basic_map_intersect(
6167 __isl_take isl_basic_map *bmap1,
6168 __isl_take isl_basic_map *bmap2);
6169 __isl_give isl_basic_map *isl_basic_map_list_intersect(
6170 __isl_take isl_basic_map_list *list);
6171 __isl_give isl_map *isl_map_intersect_params(
6172 __isl_take isl_map *map,
6173 __isl_take isl_set *params);
6174 __isl_give isl_map *isl_map_intersect_domain(
6175 __isl_take isl_map *map,
6176 __isl_take isl_set *set);
6177 __isl_give isl_map *isl_map_intersect_range(
6178 __isl_take isl_map *map,
6179 __isl_take isl_set *set);
6180 __isl_give isl_map *isl_map_intersect(
6181 __isl_take isl_map *map1,
6182 __isl_take isl_map *map2);
6183 __isl_give isl_map *
6184 isl_map_intersect_domain_factor_range(
6185 __isl_take isl_map *map,
6186 __isl_take isl_map *factor);
6187 __isl_give isl_map *
6188 isl_map_intersect_range_factor_range(
6189 __isl_take isl_map *map,
6190 __isl_take isl_map *factor);
6192 #include <isl/union_set.h>
6193 __isl_give isl_union_set *isl_union_set_intersect_params(
6194 __isl_take isl_union_set *uset,
6195 __isl_take isl_set *set);
6196 __isl_give isl_union_set *isl_union_set_intersect(
6197 __isl_take isl_union_set *uset1,
6198 __isl_take isl_union_set *uset2);
6200 #include <isl/union_map.h>
6201 __isl_give isl_union_map *isl_union_map_intersect_params(
6202 __isl_take isl_union_map *umap,
6203 __isl_take isl_set *set);
6204 __isl_give isl_union_map *isl_union_map_intersect_domain(
6205 __isl_take isl_union_map *umap,
6206 __isl_take isl_union_set *uset);
6207 __isl_give isl_union_map *isl_union_map_intersect_range(
6208 __isl_take isl_union_map *umap,
6209 __isl_take isl_union_set *uset);
6210 __isl_give isl_union_map *isl_union_map_intersect(
6211 __isl_take isl_union_map *umap1,
6212 __isl_take isl_union_map *umap2);
6213 __isl_give isl_union_map *
6214 isl_union_map_intersect_range_factor_range(
6215 __isl_take isl_union_map *umap,
6216 __isl_take isl_union_map *factor);
6218 #include <isl/aff.h>
6219 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6220 __isl_take isl_pw_aff *pa,
6221 __isl_take isl_set *set);
6222 __isl_give isl_multi_pw_aff *
6223 isl_multi_pw_aff_intersect_domain(
6224 __isl_take isl_multi_pw_aff *mpa,
6225 __isl_take isl_set *domain);
6226 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6227 __isl_take isl_pw_multi_aff *pma,
6228 __isl_take isl_set *set);
6229 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6230 __isl_take isl_union_pw_aff *upa,
6231 __isl_take isl_union_set *uset);
6232 __isl_give isl_union_pw_multi_aff *
6233 isl_union_pw_multi_aff_intersect_domain(
6234 __isl_take isl_union_pw_multi_aff *upma,
6235 __isl_take isl_union_set *uset);
6236 __isl_give isl_multi_union_pw_aff *
6237 isl_multi_union_pw_aff_intersect_domain(
6238 __isl_take isl_multi_union_pw_aff *mupa,
6239 __isl_take isl_union_set *uset);
6240 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6241 __isl_take isl_pw_aff *pa,
6242 __isl_take isl_set *set);
6243 __isl_give isl_multi_pw_aff *
6244 isl_multi_pw_aff_intersect_params(
6245 __isl_take isl_multi_pw_aff *mpa,
6246 __isl_take isl_set *set);
6247 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6248 __isl_take isl_pw_multi_aff *pma,
6249 __isl_take isl_set *set);
6250 __isl_give isl_union_pw_aff *
6251 isl_union_pw_aff_intersect_params(
6252 __isl_take isl_union_pw_aff *upa,
6253 __isl_give isl_union_pw_multi_aff *
6254 isl_union_pw_multi_aff_intersect_params(
6255 __isl_take isl_union_pw_multi_aff *upma,
6256 __isl_take isl_set *set);
6257 __isl_give isl_multi_union_pw_aff *
6258 isl_multi_union_pw_aff_intersect_params(
6259 __isl_take isl_multi_union_pw_aff *mupa,
6260 __isl_take isl_set *params);
6261 isl_multi_union_pw_aff_intersect_range(
6262 __isl_take isl_multi_union_pw_aff *mupa,
6263 __isl_take isl_set *set);
6265 #include <isl/polynomial.h>
6266 __isl_give isl_pw_qpolynomial *
6267 isl_pw_qpolynomial_intersect_domain(
6268 __isl_take isl_pw_qpolynomial *pwpq,
6269 __isl_take isl_set *set);
6270 __isl_give isl_union_pw_qpolynomial *
6271 isl_union_pw_qpolynomial_intersect_domain(
6272 __isl_take isl_union_pw_qpolynomial *upwpq,
6273 __isl_take isl_union_set *uset);
6274 __isl_give isl_union_pw_qpolynomial_fold *
6275 isl_union_pw_qpolynomial_fold_intersect_domain(
6276 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6277 __isl_take isl_union_set *uset);
6278 __isl_give isl_pw_qpolynomial *
6279 isl_pw_qpolynomial_intersect_params(
6280 __isl_take isl_pw_qpolynomial *pwpq,
6281 __isl_take isl_set *set);
6282 __isl_give isl_pw_qpolynomial_fold *
6283 isl_pw_qpolynomial_fold_intersect_params(
6284 __isl_take isl_pw_qpolynomial_fold *pwf,
6285 __isl_take isl_set *set);
6286 __isl_give isl_union_pw_qpolynomial *
6287 isl_union_pw_qpolynomial_intersect_params(
6288 __isl_take isl_union_pw_qpolynomial *upwpq,
6289 __isl_take isl_set *set);
6290 __isl_give isl_union_pw_qpolynomial_fold *
6291 isl_union_pw_qpolynomial_fold_intersect_params(
6292 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6293 __isl_take isl_set *set);
6295 The second argument to the C<_params> functions needs to be
6296 a parametric (basic) set. For the other functions, a parametric set
6297 for either argument is only allowed if the other argument is
6298 a parametric set as well.
6299 The list passed to C<isl_basic_set_list_intersect> needs to have
6300 at least one element and all elements need to live in the same space.
6301 The function C<isl_multi_union_pw_aff_intersect_range>
6302 restricts the input function to those shared domain elements
6303 that map to the specified range.
6307 #include <isl/set.h>
6308 __isl_give isl_set *isl_basic_set_union(
6309 __isl_take isl_basic_set *bset1,
6310 __isl_take isl_basic_set *bset2);
6311 __isl_give isl_set *isl_set_union(
6312 __isl_take isl_set *set1,
6313 __isl_take isl_set *set2);
6314 __isl_give isl_set *isl_set_list_union(
6315 __isl_take isl_set_list *list);
6317 #include <isl/map.h>
6318 __isl_give isl_map *isl_basic_map_union(
6319 __isl_take isl_basic_map *bmap1,
6320 __isl_take isl_basic_map *bmap2);
6321 __isl_give isl_map *isl_map_union(
6322 __isl_take isl_map *map1,
6323 __isl_take isl_map *map2);
6325 #include <isl/union_set.h>
6326 __isl_give isl_union_set *isl_union_set_union(
6327 __isl_take isl_union_set *uset1,
6328 __isl_take isl_union_set *uset2);
6329 __isl_give isl_union_set *isl_union_set_list_union(
6330 __isl_take isl_union_set_list *list);
6332 #include <isl/union_map.h>
6333 __isl_give isl_union_map *isl_union_map_union(
6334 __isl_take isl_union_map *umap1,
6335 __isl_take isl_union_map *umap2);
6337 The list passed to C<isl_set_list_union> needs to have
6338 at least one element and all elements need to live in the same space.
6340 =item * Set difference
6342 #include <isl/set.h>
6343 __isl_give isl_set *isl_set_subtract(
6344 __isl_take isl_set *set1,
6345 __isl_take isl_set *set2);
6347 #include <isl/map.h>
6348 __isl_give isl_map *isl_map_subtract(
6349 __isl_take isl_map *map1,
6350 __isl_take isl_map *map2);
6351 __isl_give isl_map *isl_map_subtract_domain(
6352 __isl_take isl_map *map,
6353 __isl_take isl_set *dom);
6354 __isl_give isl_map *isl_map_subtract_range(
6355 __isl_take isl_map *map,
6356 __isl_take isl_set *dom);
6358 #include <isl/union_set.h>
6359 __isl_give isl_union_set *isl_union_set_subtract(
6360 __isl_take isl_union_set *uset1,
6361 __isl_take isl_union_set *uset2);
6363 #include <isl/union_map.h>
6364 __isl_give isl_union_map *isl_union_map_subtract(
6365 __isl_take isl_union_map *umap1,
6366 __isl_take isl_union_map *umap2);
6367 __isl_give isl_union_map *isl_union_map_subtract_domain(
6368 __isl_take isl_union_map *umap,
6369 __isl_take isl_union_set *dom);
6370 __isl_give isl_union_map *isl_union_map_subtract_range(
6371 __isl_take isl_union_map *umap,
6372 __isl_take isl_union_set *dom);
6374 #include <isl/aff.h>
6375 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6376 __isl_take isl_pw_aff *pa,
6377 __isl_take isl_set *set);
6378 __isl_give isl_pw_multi_aff *
6379 isl_pw_multi_aff_subtract_domain(
6380 __isl_take isl_pw_multi_aff *pma,
6381 __isl_take isl_set *set);
6382 __isl_give isl_union_pw_aff *
6383 isl_union_pw_aff_subtract_domain(
6384 __isl_take isl_union_pw_aff *upa,
6385 __isl_take isl_union_set *uset);
6386 __isl_give isl_union_pw_multi_aff *
6387 isl_union_pw_multi_aff_subtract_domain(
6388 __isl_take isl_union_pw_multi_aff *upma,
6389 __isl_take isl_set *set);
6391 #include <isl/polynomial.h>
6392 __isl_give isl_pw_qpolynomial *
6393 isl_pw_qpolynomial_subtract_domain(
6394 __isl_take isl_pw_qpolynomial *pwpq,
6395 __isl_take isl_set *set);
6396 __isl_give isl_pw_qpolynomial_fold *
6397 isl_pw_qpolynomial_fold_subtract_domain(
6398 __isl_take isl_pw_qpolynomial_fold *pwf,
6399 __isl_take isl_set *set);
6400 __isl_give isl_union_pw_qpolynomial *
6401 isl_union_pw_qpolynomial_subtract_domain(
6402 __isl_take isl_union_pw_qpolynomial *upwpq,
6403 __isl_take isl_union_set *uset);
6404 __isl_give isl_union_pw_qpolynomial_fold *
6405 isl_union_pw_qpolynomial_fold_subtract_domain(
6406 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6407 __isl_take isl_union_set *uset);
6411 #include <isl/space.h>
6412 __isl_give isl_space *isl_space_join(
6413 __isl_take isl_space *left,
6414 __isl_take isl_space *right);
6416 #include <isl/map.h>
6417 __isl_give isl_basic_set *isl_basic_set_apply(
6418 __isl_take isl_basic_set *bset,
6419 __isl_take isl_basic_map *bmap);
6420 __isl_give isl_set *isl_set_apply(
6421 __isl_take isl_set *set,
6422 __isl_take isl_map *map);
6423 __isl_give isl_union_set *isl_union_set_apply(
6424 __isl_take isl_union_set *uset,
6425 __isl_take isl_union_map *umap);
6426 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6427 __isl_take isl_basic_map *bmap1,
6428 __isl_take isl_basic_map *bmap2);
6429 __isl_give isl_basic_map *isl_basic_map_apply_range(
6430 __isl_take isl_basic_map *bmap1,
6431 __isl_take isl_basic_map *bmap2);
6432 __isl_give isl_map *isl_map_apply_domain(
6433 __isl_take isl_map *map1,
6434 __isl_take isl_map *map2);
6435 __isl_give isl_map *isl_map_apply_range(
6436 __isl_take isl_map *map1,
6437 __isl_take isl_map *map2);
6439 #include <isl/union_map.h>
6440 __isl_give isl_union_map *isl_union_map_apply_domain(
6441 __isl_take isl_union_map *umap1,
6442 __isl_take isl_union_map *umap2);
6443 __isl_give isl_union_map *isl_union_map_apply_range(
6444 __isl_take isl_union_map *umap1,
6445 __isl_take isl_union_map *umap2);
6447 #include <isl/aff.h>
6448 __isl_give isl_union_pw_aff *
6449 isl_multi_union_pw_aff_apply_aff(
6450 __isl_take isl_multi_union_pw_aff *mupa,
6451 __isl_take isl_aff *aff);
6452 __isl_give isl_union_pw_aff *
6453 isl_multi_union_pw_aff_apply_pw_aff(
6454 __isl_take isl_multi_union_pw_aff *mupa,
6455 __isl_take isl_pw_aff *pa);
6456 __isl_give isl_multi_union_pw_aff *
6457 isl_multi_union_pw_aff_apply_multi_aff(
6458 __isl_take isl_multi_union_pw_aff *mupa,
6459 __isl_take isl_multi_aff *ma);
6460 __isl_give isl_multi_union_pw_aff *
6461 isl_multi_union_pw_aff_apply_pw_multi_aff(
6462 __isl_take isl_multi_union_pw_aff *mupa,
6463 __isl_take isl_pw_multi_aff *pma);
6465 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6466 over the shared domain of the elements of the input. The dimension is
6467 required to be greater than zero.
6468 The C<isl_multi_union_pw_aff> argument of
6469 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6470 but only if the range of the C<isl_multi_aff> argument
6471 is also zero-dimensional.
6472 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6474 #include <isl/polynomial.h>
6475 __isl_give isl_pw_qpolynomial_fold *
6476 isl_set_apply_pw_qpolynomial_fold(
6477 __isl_take isl_set *set,
6478 __isl_take isl_pw_qpolynomial_fold *pwf,
6480 __isl_give isl_pw_qpolynomial_fold *
6481 isl_map_apply_pw_qpolynomial_fold(
6482 __isl_take isl_map *map,
6483 __isl_take isl_pw_qpolynomial_fold *pwf,
6485 __isl_give isl_union_pw_qpolynomial_fold *
6486 isl_union_set_apply_union_pw_qpolynomial_fold(
6487 __isl_take isl_union_set *uset,
6488 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6490 __isl_give isl_union_pw_qpolynomial_fold *
6491 isl_union_map_apply_union_pw_qpolynomial_fold(
6492 __isl_take isl_union_map *umap,
6493 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6496 The functions taking a map
6497 compose the given map with the given piecewise quasipolynomial reduction.
6498 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6499 over all elements in the intersection of the range of the map
6500 and the domain of the piecewise quasipolynomial reduction
6501 as a function of an element in the domain of the map.
6502 The functions taking a set compute a bound over all elements in the
6503 intersection of the set and the domain of the
6504 piecewise quasipolynomial reduction.
6508 #include <isl/set.h>
6509 __isl_give isl_basic_set *
6510 isl_basic_set_preimage_multi_aff(
6511 __isl_take isl_basic_set *bset,
6512 __isl_take isl_multi_aff *ma);
6513 __isl_give isl_set *isl_set_preimage_multi_aff(
6514 __isl_take isl_set *set,
6515 __isl_take isl_multi_aff *ma);
6516 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6517 __isl_take isl_set *set,
6518 __isl_take isl_pw_multi_aff *pma);
6519 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6520 __isl_take isl_set *set,
6521 __isl_take isl_multi_pw_aff *mpa);
6523 #include <isl/union_set.h>
6524 __isl_give isl_union_set *
6525 isl_union_set_preimage_multi_aff(
6526 __isl_take isl_union_set *uset,
6527 __isl_take isl_multi_aff *ma);
6528 __isl_give isl_union_set *
6529 isl_union_set_preimage_pw_multi_aff(
6530 __isl_take isl_union_set *uset,
6531 __isl_take isl_pw_multi_aff *pma);
6532 __isl_give isl_union_set *
6533 isl_union_set_preimage_union_pw_multi_aff(
6534 __isl_take isl_union_set *uset,
6535 __isl_take isl_union_pw_multi_aff *upma);
6537 #include <isl/map.h>
6538 __isl_give isl_basic_map *
6539 isl_basic_map_preimage_domain_multi_aff(
6540 __isl_take isl_basic_map *bmap,
6541 __isl_take isl_multi_aff *ma);
6542 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6543 __isl_take isl_map *map,
6544 __isl_take isl_multi_aff *ma);
6545 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6546 __isl_take isl_map *map,
6547 __isl_take isl_multi_aff *ma);
6548 __isl_give isl_map *
6549 isl_map_preimage_domain_pw_multi_aff(
6550 __isl_take isl_map *map,
6551 __isl_take isl_pw_multi_aff *pma);
6552 __isl_give isl_map *
6553 isl_map_preimage_range_pw_multi_aff(
6554 __isl_take isl_map *map,
6555 __isl_take isl_pw_multi_aff *pma);
6556 __isl_give isl_map *
6557 isl_map_preimage_domain_multi_pw_aff(
6558 __isl_take isl_map *map,
6559 __isl_take isl_multi_pw_aff *mpa);
6560 __isl_give isl_basic_map *
6561 isl_basic_map_preimage_range_multi_aff(
6562 __isl_take isl_basic_map *bmap,
6563 __isl_take isl_multi_aff *ma);
6565 #include <isl/union_map.h>
6566 __isl_give isl_union_map *
6567 isl_union_map_preimage_domain_multi_aff(
6568 __isl_take isl_union_map *umap,
6569 __isl_take isl_multi_aff *ma);
6570 __isl_give isl_union_map *
6571 isl_union_map_preimage_range_multi_aff(
6572 __isl_take isl_union_map *umap,
6573 __isl_take isl_multi_aff *ma);
6574 __isl_give isl_union_map *
6575 isl_union_map_preimage_domain_pw_multi_aff(
6576 __isl_take isl_union_map *umap,
6577 __isl_take isl_pw_multi_aff *pma);
6578 __isl_give isl_union_map *
6579 isl_union_map_preimage_range_pw_multi_aff(
6580 __isl_take isl_union_map *umap,
6581 __isl_take isl_pw_multi_aff *pma);
6582 __isl_give isl_union_map *
6583 isl_union_map_preimage_domain_union_pw_multi_aff(
6584 __isl_take isl_union_map *umap,
6585 __isl_take isl_union_pw_multi_aff *upma);
6586 __isl_give isl_union_map *
6587 isl_union_map_preimage_range_union_pw_multi_aff(
6588 __isl_take isl_union_map *umap,
6589 __isl_take isl_union_pw_multi_aff *upma);
6591 These functions compute the preimage of the given set or map domain/range under
6592 the given function. In other words, the expression is plugged
6593 into the set description or into the domain/range of the map.
6597 #include <isl/aff.h>
6598 __isl_give isl_aff *isl_aff_pullback_aff(
6599 __isl_take isl_aff *aff1,
6600 __isl_take isl_aff *aff2);
6601 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6602 __isl_take isl_aff *aff,
6603 __isl_take isl_multi_aff *ma);
6604 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6605 __isl_take isl_pw_aff *pa,
6606 __isl_take isl_multi_aff *ma);
6607 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6608 __isl_take isl_pw_aff *pa,
6609 __isl_take isl_pw_multi_aff *pma);
6610 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6611 __isl_take isl_pw_aff *pa,
6612 __isl_take isl_multi_pw_aff *mpa);
6613 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6614 __isl_take isl_multi_aff *ma1,
6615 __isl_take isl_multi_aff *ma2);
6616 __isl_give isl_pw_multi_aff *
6617 isl_pw_multi_aff_pullback_multi_aff(
6618 __isl_take isl_pw_multi_aff *pma,
6619 __isl_take isl_multi_aff *ma);
6620 __isl_give isl_multi_pw_aff *
6621 isl_multi_pw_aff_pullback_multi_aff(
6622 __isl_take isl_multi_pw_aff *mpa,
6623 __isl_take isl_multi_aff *ma);
6624 __isl_give isl_pw_multi_aff *
6625 isl_pw_multi_aff_pullback_pw_multi_aff(
6626 __isl_take isl_pw_multi_aff *pma1,
6627 __isl_take isl_pw_multi_aff *pma2);
6628 __isl_give isl_multi_pw_aff *
6629 isl_multi_pw_aff_pullback_pw_multi_aff(
6630 __isl_take isl_multi_pw_aff *mpa,
6631 __isl_take isl_pw_multi_aff *pma);
6632 __isl_give isl_multi_pw_aff *
6633 isl_multi_pw_aff_pullback_multi_pw_aff(
6634 __isl_take isl_multi_pw_aff *mpa1,
6635 __isl_take isl_multi_pw_aff *mpa2);
6636 __isl_give isl_union_pw_aff *
6637 isl_union_pw_aff_pullback_union_pw_multi_aff(
6638 __isl_take isl_union_pw_aff *upa,
6639 __isl_take isl_union_pw_multi_aff *upma);
6640 __isl_give isl_union_pw_multi_aff *
6641 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6642 __isl_take isl_union_pw_multi_aff *upma1,
6643 __isl_take isl_union_pw_multi_aff *upma2);
6644 __isl_give isl_multi_union_pw_aff *
6645 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6646 __isl_take isl_multi_union_pw_aff *mupa,
6647 __isl_take isl_union_pw_multi_aff *upma);
6649 These functions precompose the first expression by the second function.
6650 In other words, the second function is plugged
6651 into the first expression.
6655 #include <isl/aff.h>
6656 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6657 __isl_take isl_aff *aff1,
6658 __isl_take isl_aff *aff2);
6659 __isl_give isl_set *isl_aff_eq_set(
6660 __isl_take isl_aff *aff1,
6661 __isl_take isl_aff *aff2);
6662 __isl_give isl_set *isl_aff_ne_set(
6663 __isl_take isl_aff *aff1,
6664 __isl_take isl_aff *aff2);
6665 __isl_give isl_basic_set *isl_aff_le_basic_set(
6666 __isl_take isl_aff *aff1,
6667 __isl_take isl_aff *aff2);
6668 __isl_give isl_set *isl_aff_le_set(
6669 __isl_take isl_aff *aff1,
6670 __isl_take isl_aff *aff2);
6671 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6672 __isl_take isl_aff *aff1,
6673 __isl_take isl_aff *aff2);
6674 __isl_give isl_set *isl_aff_lt_set(
6675 __isl_take isl_aff *aff1,
6676 __isl_take isl_aff *aff2);
6677 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6678 __isl_take isl_aff *aff1,
6679 __isl_take isl_aff *aff2);
6680 __isl_give isl_set *isl_aff_ge_set(
6681 __isl_take isl_aff *aff1,
6682 __isl_take isl_aff *aff2);
6683 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6684 __isl_take isl_aff *aff1,
6685 __isl_take isl_aff *aff2);
6686 __isl_give isl_set *isl_aff_gt_set(
6687 __isl_take isl_aff *aff1,
6688 __isl_take isl_aff *aff2);
6689 __isl_give isl_set *isl_pw_aff_eq_set(
6690 __isl_take isl_pw_aff *pwaff1,
6691 __isl_take isl_pw_aff *pwaff2);
6692 __isl_give isl_set *isl_pw_aff_ne_set(
6693 __isl_take isl_pw_aff *pwaff1,
6694 __isl_take isl_pw_aff *pwaff2);
6695 __isl_give isl_set *isl_pw_aff_le_set(
6696 __isl_take isl_pw_aff *pwaff1,
6697 __isl_take isl_pw_aff *pwaff2);
6698 __isl_give isl_set *isl_pw_aff_lt_set(
6699 __isl_take isl_pw_aff *pwaff1,
6700 __isl_take isl_pw_aff *pwaff2);
6701 __isl_give isl_set *isl_pw_aff_ge_set(
6702 __isl_take isl_pw_aff *pwaff1,
6703 __isl_take isl_pw_aff *pwaff2);
6704 __isl_give isl_set *isl_pw_aff_gt_set(
6705 __isl_take isl_pw_aff *pwaff1,
6706 __isl_take isl_pw_aff *pwaff2);
6708 __isl_give isl_set *isl_multi_aff_lex_le_set(
6709 __isl_take isl_multi_aff *ma1,
6710 __isl_take isl_multi_aff *ma2);
6711 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6712 __isl_take isl_multi_aff *ma1,
6713 __isl_take isl_multi_aff *ma2);
6714 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6715 __isl_take isl_multi_aff *ma1,
6716 __isl_take isl_multi_aff *ma2);
6717 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6718 __isl_take isl_multi_aff *ma1,
6719 __isl_take isl_multi_aff *ma2);
6721 __isl_give isl_set *isl_pw_aff_list_eq_set(
6722 __isl_take isl_pw_aff_list *list1,
6723 __isl_take isl_pw_aff_list *list2);
6724 __isl_give isl_set *isl_pw_aff_list_ne_set(
6725 __isl_take isl_pw_aff_list *list1,
6726 __isl_take isl_pw_aff_list *list2);
6727 __isl_give isl_set *isl_pw_aff_list_le_set(
6728 __isl_take isl_pw_aff_list *list1,
6729 __isl_take isl_pw_aff_list *list2);
6730 __isl_give isl_set *isl_pw_aff_list_lt_set(
6731 __isl_take isl_pw_aff_list *list1,
6732 __isl_take isl_pw_aff_list *list2);
6733 __isl_give isl_set *isl_pw_aff_list_ge_set(
6734 __isl_take isl_pw_aff_list *list1,
6735 __isl_take isl_pw_aff_list *list2);
6736 __isl_give isl_set *isl_pw_aff_list_gt_set(
6737 __isl_take isl_pw_aff_list *list1,
6738 __isl_take isl_pw_aff_list *list2);
6740 The function C<isl_aff_ge_basic_set> returns a basic set
6741 containing those elements in the shared space
6742 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6743 The function C<isl_pw_aff_ge_set> returns a set
6744 containing those elements in the shared domain
6745 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6746 greater than or equal to C<pwaff2>.
6747 The function C<isl_multi_aff_lex_le_set> returns a set
6748 containing those elements in the shared domain space
6749 where C<ma1> is lexicographically smaller than or
6751 The functions operating on C<isl_pw_aff_list> apply the corresponding
6752 C<isl_pw_aff> function to each pair of elements in the two lists.
6754 #include <isl/aff.h>
6755 __isl_give isl_map *isl_pw_aff_eq_map(
6756 __isl_take isl_pw_aff *pa1,
6757 __isl_take isl_pw_aff *pa2);
6758 __isl_give isl_map *isl_pw_aff_lt_map(
6759 __isl_take isl_pw_aff *pa1,
6760 __isl_take isl_pw_aff *pa2);
6761 __isl_give isl_map *isl_pw_aff_gt_map(
6762 __isl_take isl_pw_aff *pa1,
6763 __isl_take isl_pw_aff *pa2);
6765 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6766 __isl_take isl_multi_pw_aff *mpa1,
6767 __isl_take isl_multi_pw_aff *mpa2);
6768 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6769 __isl_take isl_multi_pw_aff *mpa1,
6770 __isl_take isl_multi_pw_aff *mpa2);
6771 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6772 __isl_take isl_multi_pw_aff *mpa1,
6773 __isl_take isl_multi_pw_aff *mpa2);
6775 These functions return a map between domain elements of the arguments
6776 where the function values satisfy the given relation.
6778 #include <isl/union_map.h>
6779 __isl_give isl_union_map *
6780 isl_union_map_eq_at_multi_union_pw_aff(
6781 __isl_take isl_union_map *umap,
6782 __isl_take isl_multi_union_pw_aff *mupa);
6783 __isl_give isl_union_map *
6784 isl_union_map_lex_lt_at_multi_union_pw_aff(
6785 __isl_take isl_union_map *umap,
6786 __isl_take isl_multi_union_pw_aff *mupa);
6787 __isl_give isl_union_map *
6788 isl_union_map_lex_gt_at_multi_union_pw_aff(
6789 __isl_take isl_union_map *umap,
6790 __isl_take isl_multi_union_pw_aff *mupa);
6792 These functions select the subset of elements in the union map
6793 that have an equal or lexicographically smaller function value.
6795 =item * Cartesian Product
6797 #include <isl/space.h>
6798 __isl_give isl_space *isl_space_product(
6799 __isl_take isl_space *space1,
6800 __isl_take isl_space *space2);
6801 __isl_give isl_space *isl_space_domain_product(
6802 __isl_take isl_space *space1,
6803 __isl_take isl_space *space2);
6804 __isl_give isl_space *isl_space_range_product(
6805 __isl_take isl_space *space1,
6806 __isl_take isl_space *space2);
6809 C<isl_space_product>, C<isl_space_domain_product>
6810 and C<isl_space_range_product> take pairs or relation spaces and
6811 produce a single relations space, where either the domain, the range
6812 or both domain and range are wrapped spaces of relations between
6813 the domains and/or ranges of the input spaces.
6814 If the product is only constructed over the domain or the range
6815 then the ranges or the domains of the inputs should be the same.
6816 The function C<isl_space_product> also accepts a pair of set spaces,
6817 in which case it returns a wrapped space of a relation between the
6820 #include <isl/set.h>
6821 __isl_give isl_set *isl_set_product(
6822 __isl_take isl_set *set1,
6823 __isl_take isl_set *set2);
6825 #include <isl/map.h>
6826 __isl_give isl_basic_map *isl_basic_map_domain_product(
6827 __isl_take isl_basic_map *bmap1,
6828 __isl_take isl_basic_map *bmap2);
6829 __isl_give isl_basic_map *isl_basic_map_range_product(
6830 __isl_take isl_basic_map *bmap1,
6831 __isl_take isl_basic_map *bmap2);
6832 __isl_give isl_basic_map *isl_basic_map_product(
6833 __isl_take isl_basic_map *bmap1,
6834 __isl_take isl_basic_map *bmap2);
6835 __isl_give isl_map *isl_map_domain_product(
6836 __isl_take isl_map *map1,
6837 __isl_take isl_map *map2);
6838 __isl_give isl_map *isl_map_range_product(
6839 __isl_take isl_map *map1,
6840 __isl_take isl_map *map2);
6841 __isl_give isl_map *isl_map_product(
6842 __isl_take isl_map *map1,
6843 __isl_take isl_map *map2);
6845 #include <isl/union_set.h>
6846 __isl_give isl_union_set *isl_union_set_product(
6847 __isl_take isl_union_set *uset1,
6848 __isl_take isl_union_set *uset2);
6850 #include <isl/union_map.h>
6851 __isl_give isl_union_map *isl_union_map_domain_product(
6852 __isl_take isl_union_map *umap1,
6853 __isl_take isl_union_map *umap2);
6854 __isl_give isl_union_map *isl_union_map_range_product(
6855 __isl_take isl_union_map *umap1,
6856 __isl_take isl_union_map *umap2);
6857 __isl_give isl_union_map *isl_union_map_product(
6858 __isl_take isl_union_map *umap1,
6859 __isl_take isl_union_map *umap2);
6861 #include <isl/val.h>
6862 __isl_give isl_multi_val *isl_multi_val_range_product(
6863 __isl_take isl_multi_val *mv1,
6864 __isl_take isl_multi_val *mv2);
6865 __isl_give isl_multi_val *isl_multi_val_product(
6866 __isl_take isl_multi_val *mv1,
6867 __isl_take isl_multi_val *mv2);
6869 #include <isl/aff.h>
6870 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6871 __isl_take isl_multi_aff *ma1,
6872 __isl_take isl_multi_aff *ma2);
6873 __isl_give isl_multi_aff *isl_multi_aff_product(
6874 __isl_take isl_multi_aff *ma1,
6875 __isl_take isl_multi_aff *ma2);
6876 __isl_give isl_multi_pw_aff *
6877 isl_multi_pw_aff_range_product(
6878 __isl_take isl_multi_pw_aff *mpa1,
6879 __isl_take isl_multi_pw_aff *mpa2);
6880 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6881 __isl_take isl_multi_pw_aff *mpa1,
6882 __isl_take isl_multi_pw_aff *mpa2);
6883 __isl_give isl_pw_multi_aff *
6884 isl_pw_multi_aff_range_product(
6885 __isl_take isl_pw_multi_aff *pma1,
6886 __isl_take isl_pw_multi_aff *pma2);
6887 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6888 __isl_take isl_pw_multi_aff *pma1,
6889 __isl_take isl_pw_multi_aff *pma2);
6890 __isl_give isl_multi_union_pw_aff *
6891 isl_multi_union_pw_aff_range_product(
6892 __isl_take isl_multi_union_pw_aff *mupa1,
6893 __isl_take isl_multi_union_pw_aff *mupa2);
6895 The above functions compute the cross product of the given
6896 sets, relations or functions. The domains and ranges of the results
6897 are wrapped maps between domains and ranges of the inputs.
6898 To obtain a ``flat'' product, use the following functions
6901 #include <isl/set.h>
6902 __isl_give isl_basic_set *isl_basic_set_flat_product(
6903 __isl_take isl_basic_set *bset1,
6904 __isl_take isl_basic_set *bset2);
6905 __isl_give isl_set *isl_set_flat_product(
6906 __isl_take isl_set *set1,
6907 __isl_take isl_set *set2);
6909 #include <isl/map.h>
6910 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6911 __isl_take isl_basic_map *bmap1,
6912 __isl_take isl_basic_map *bmap2);
6913 __isl_give isl_map *isl_map_flat_domain_product(
6914 __isl_take isl_map *map1,
6915 __isl_take isl_map *map2);
6916 __isl_give isl_map *isl_map_flat_range_product(
6917 __isl_take isl_map *map1,
6918 __isl_take isl_map *map2);
6919 __isl_give isl_basic_map *isl_basic_map_flat_product(
6920 __isl_take isl_basic_map *bmap1,
6921 __isl_take isl_basic_map *bmap2);
6922 __isl_give isl_map *isl_map_flat_product(
6923 __isl_take isl_map *map1,
6924 __isl_take isl_map *map2);
6926 #include <isl/union_map.h>
6927 __isl_give isl_union_map *
6928 isl_union_map_flat_domain_product(
6929 __isl_take isl_union_map *umap1,
6930 __isl_take isl_union_map *umap2);
6931 __isl_give isl_union_map *
6932 isl_union_map_flat_range_product(
6933 __isl_take isl_union_map *umap1,
6934 __isl_take isl_union_map *umap2);
6936 #include <isl/val.h>
6937 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6938 __isl_take isl_multi_val *mv1,
6939 __isl_take isl_multi_val *mv2);
6941 #include <isl/aff.h>
6942 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6943 __isl_take isl_multi_aff *ma1,
6944 __isl_take isl_multi_aff *ma2);
6945 __isl_give isl_pw_multi_aff *
6946 isl_pw_multi_aff_flat_range_product(
6947 __isl_take isl_pw_multi_aff *pma1,
6948 __isl_take isl_pw_multi_aff *pma2);
6949 __isl_give isl_multi_pw_aff *
6950 isl_multi_pw_aff_flat_range_product(
6951 __isl_take isl_multi_pw_aff *mpa1,
6952 __isl_take isl_multi_pw_aff *mpa2);
6953 __isl_give isl_union_pw_multi_aff *
6954 isl_union_pw_multi_aff_flat_range_product(
6955 __isl_take isl_union_pw_multi_aff *upma1,
6956 __isl_take isl_union_pw_multi_aff *upma2);
6957 __isl_give isl_multi_union_pw_aff *
6958 isl_multi_union_pw_aff_flat_range_product(
6959 __isl_take isl_multi_union_pw_aff *mupa1,
6960 __isl_take isl_multi_union_pw_aff *mupa2);
6962 #include <isl/space.h>
6963 __isl_give isl_space *isl_space_factor_domain(
6964 __isl_take isl_space *space);
6965 __isl_give isl_space *isl_space_factor_range(
6966 __isl_take isl_space *space);
6967 __isl_give isl_space *isl_space_domain_factor_domain(
6968 __isl_take isl_space *space);
6969 __isl_give isl_space *isl_space_domain_factor_range(
6970 __isl_take isl_space *space);
6971 __isl_give isl_space *isl_space_range_factor_domain(
6972 __isl_take isl_space *space);
6973 __isl_give isl_space *isl_space_range_factor_range(
6974 __isl_take isl_space *space);
6976 The functions C<isl_space_range_factor_domain> and
6977 C<isl_space_range_factor_range> extract the two arguments from
6978 the result of a call to C<isl_space_range_product>.
6980 The arguments of a call to a product can be extracted
6981 from the result using the following functions.
6983 #include <isl/map.h>
6984 __isl_give isl_map *isl_map_factor_domain(
6985 __isl_take isl_map *map);
6986 __isl_give isl_map *isl_map_factor_range(
6987 __isl_take isl_map *map);
6988 __isl_give isl_map *isl_map_domain_factor_domain(
6989 __isl_take isl_map *map);
6990 __isl_give isl_map *isl_map_domain_factor_range(
6991 __isl_take isl_map *map);
6992 __isl_give isl_map *isl_map_range_factor_domain(
6993 __isl_take isl_map *map);
6994 __isl_give isl_map *isl_map_range_factor_range(
6995 __isl_take isl_map *map);
6997 #include <isl/union_map.h>
6998 __isl_give isl_union_map *isl_union_map_factor_domain(
6999 __isl_take isl_union_map *umap);
7000 __isl_give isl_union_map *isl_union_map_factor_range(
7001 __isl_take isl_union_map *umap);
7002 __isl_give isl_union_map *
7003 isl_union_map_domain_factor_domain(
7004 __isl_take isl_union_map *umap);
7005 __isl_give isl_union_map *
7006 isl_union_map_domain_factor_range(
7007 __isl_take isl_union_map *umap);
7008 __isl_give isl_union_map *
7009 isl_union_map_range_factor_domain(
7010 __isl_take isl_union_map *umap);
7011 __isl_give isl_union_map *
7012 isl_union_map_range_factor_range(
7013 __isl_take isl_union_map *umap);
7015 #include <isl/val.h>
7016 __isl_give isl_multi_val *isl_multi_val_factor_range(
7017 __isl_take isl_multi_val *mv);
7018 __isl_give isl_multi_val *
7019 isl_multi_val_range_factor_domain(
7020 __isl_take isl_multi_val *mv);
7021 __isl_give isl_multi_val *
7022 isl_multi_val_range_factor_range(
7023 __isl_take isl_multi_val *mv);
7025 #include <isl/aff.h>
7026 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
7027 __isl_take isl_multi_aff *ma);
7028 __isl_give isl_multi_aff *
7029 isl_multi_aff_range_factor_domain(
7030 __isl_take isl_multi_aff *ma);
7031 __isl_give isl_multi_aff *
7032 isl_multi_aff_range_factor_range(
7033 __isl_take isl_multi_aff *ma);
7034 __isl_give isl_multi_pw_aff *
7035 isl_multi_pw_aff_factor_range(
7036 __isl_take isl_multi_pw_aff *mpa);
7037 __isl_give isl_multi_pw_aff *
7038 isl_multi_pw_aff_range_factor_domain(
7039 __isl_take isl_multi_pw_aff *mpa);
7040 __isl_give isl_multi_pw_aff *
7041 isl_multi_pw_aff_range_factor_range(
7042 __isl_take isl_multi_pw_aff *mpa);
7043 __isl_give isl_multi_union_pw_aff *
7044 isl_multi_union_pw_aff_factor_range(
7045 __isl_take isl_multi_union_pw_aff *mupa);
7046 __isl_give isl_multi_union_pw_aff *
7047 isl_multi_union_pw_aff_range_factor_domain(
7048 __isl_take isl_multi_union_pw_aff *mupa);
7049 __isl_give isl_multi_union_pw_aff *
7050 isl_multi_union_pw_aff_range_factor_range(
7051 __isl_take isl_multi_union_pw_aff *mupa);
7053 The splice functions are a generalization of the flat product functions,
7054 where the second argument may be inserted at any position inside
7055 the first argument rather than being placed at the end.
7056 The functions C<isl_multi_val_factor_range>,
7057 C<isl_multi_aff_factor_range>,
7058 C<isl_multi_pw_aff_factor_range> and
7059 C<isl_multi_union_pw_aff_factor_range>
7060 take functions that live in a set space.
7062 #include <isl/val.h>
7063 __isl_give isl_multi_val *isl_multi_val_range_splice(
7064 __isl_take isl_multi_val *mv1, unsigned pos,
7065 __isl_take isl_multi_val *mv2);
7067 #include <isl/aff.h>
7068 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
7069 __isl_take isl_multi_aff *ma1, unsigned pos,
7070 __isl_take isl_multi_aff *ma2);
7071 __isl_give isl_multi_aff *isl_multi_aff_splice(
7072 __isl_take isl_multi_aff *ma1,
7073 unsigned in_pos, unsigned out_pos,
7074 __isl_take isl_multi_aff *ma2);
7075 __isl_give isl_multi_pw_aff *
7076 isl_multi_pw_aff_range_splice(
7077 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
7078 __isl_take isl_multi_pw_aff *mpa2);
7079 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
7080 __isl_take isl_multi_pw_aff *mpa1,
7081 unsigned in_pos, unsigned out_pos,
7082 __isl_take isl_multi_pw_aff *mpa2);
7083 __isl_give isl_multi_union_pw_aff *
7084 isl_multi_union_pw_aff_range_splice(
7085 __isl_take isl_multi_union_pw_aff *mupa1,
7087 __isl_take isl_multi_union_pw_aff *mupa2);
7089 =item * Simplification
7091 When applied to a set or relation,
7092 the gist operation returns a set or relation that has the
7093 same intersection with the context as the input set or relation.
7094 Any implicit equality in the intersection is made explicit in the result,
7095 while all inequalities that are redundant with respect to the intersection
7097 In case of union sets and relations, the gist operation is performed
7100 When applied to a function,
7101 the gist operation applies the set gist operation to each of
7102 the cells in the domain of the input piecewise expression.
7103 The context is also exploited
7104 to simplify the expression associated to each cell.
7106 #include <isl/set.h>
7107 __isl_give isl_basic_set *isl_basic_set_gist(
7108 __isl_take isl_basic_set *bset,
7109 __isl_take isl_basic_set *context);
7110 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
7111 __isl_take isl_set *context);
7112 __isl_give isl_set *isl_set_gist_params(
7113 __isl_take isl_set *set,
7114 __isl_take isl_set *context);
7116 #include <isl/map.h>
7117 __isl_give isl_basic_map *isl_basic_map_gist(
7118 __isl_take isl_basic_map *bmap,
7119 __isl_take isl_basic_map *context);
7120 __isl_give isl_basic_map *isl_basic_map_gist_domain(
7121 __isl_take isl_basic_map *bmap,
7122 __isl_take isl_basic_set *context);
7123 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
7124 __isl_take isl_map *context);
7125 __isl_give isl_map *isl_map_gist_params(
7126 __isl_take isl_map *map,
7127 __isl_take isl_set *context);
7128 __isl_give isl_map *isl_map_gist_domain(
7129 __isl_take isl_map *map,
7130 __isl_take isl_set *context);
7131 __isl_give isl_map *isl_map_gist_range(
7132 __isl_take isl_map *map,
7133 __isl_take isl_set *context);
7135 #include <isl/union_set.h>
7136 __isl_give isl_union_set *isl_union_set_gist(
7137 __isl_take isl_union_set *uset,
7138 __isl_take isl_union_set *context);
7139 __isl_give isl_union_set *isl_union_set_gist_params(
7140 __isl_take isl_union_set *uset,
7141 __isl_take isl_set *set);
7143 #include <isl/union_map.h>
7144 __isl_give isl_union_map *isl_union_map_gist(
7145 __isl_take isl_union_map *umap,
7146 __isl_take isl_union_map *context);
7147 __isl_give isl_union_map *isl_union_map_gist_params(
7148 __isl_take isl_union_map *umap,
7149 __isl_take isl_set *set);
7150 __isl_give isl_union_map *isl_union_map_gist_domain(
7151 __isl_take isl_union_map *umap,
7152 __isl_take isl_union_set *uset);
7153 __isl_give isl_union_map *isl_union_map_gist_range(
7154 __isl_take isl_union_map *umap,
7155 __isl_take isl_union_set *uset);
7157 #include <isl/aff.h>
7158 __isl_give isl_aff *isl_aff_gist_params(
7159 __isl_take isl_aff *aff,
7160 __isl_take isl_set *context);
7161 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
7162 __isl_take isl_set *context);
7163 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
7164 __isl_take isl_multi_aff *maff,
7165 __isl_take isl_set *context);
7166 __isl_give isl_multi_aff *isl_multi_aff_gist(
7167 __isl_take isl_multi_aff *maff,
7168 __isl_take isl_set *context);
7169 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
7170 __isl_take isl_pw_aff *pwaff,
7171 __isl_take isl_set *context);
7172 __isl_give isl_pw_aff *isl_pw_aff_gist(
7173 __isl_take isl_pw_aff *pwaff,
7174 __isl_take isl_set *context);
7175 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
7176 __isl_take isl_pw_multi_aff *pma,
7177 __isl_take isl_set *set);
7178 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
7179 __isl_take isl_pw_multi_aff *pma,
7180 __isl_take isl_set *set);
7181 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
7182 __isl_take isl_multi_pw_aff *mpa,
7183 __isl_take isl_set *set);
7184 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
7185 __isl_take isl_multi_pw_aff *mpa,
7186 __isl_take isl_set *set);
7187 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
7188 __isl_take isl_union_pw_aff *upa,
7189 __isl_take isl_union_set *context);
7190 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
7191 __isl_take isl_union_pw_aff *upa,
7192 __isl_take isl_set *context);
7193 __isl_give isl_union_pw_multi_aff *
7194 isl_union_pw_multi_aff_gist_params(
7195 __isl_take isl_union_pw_multi_aff *upma,
7196 __isl_take isl_set *context);
7197 __isl_give isl_union_pw_multi_aff *
7198 isl_union_pw_multi_aff_gist(
7199 __isl_take isl_union_pw_multi_aff *upma,
7200 __isl_take isl_union_set *context);
7201 __isl_give isl_multi_union_pw_aff *
7202 isl_multi_union_pw_aff_gist_params(
7203 __isl_take isl_multi_union_pw_aff *aff,
7204 __isl_take isl_set *context);
7205 __isl_give isl_multi_union_pw_aff *
7206 isl_multi_union_pw_aff_gist(
7207 __isl_take isl_multi_union_pw_aff *aff,
7208 __isl_take isl_union_set *context);
7210 #include <isl/polynomial.h>
7211 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
7212 __isl_take isl_qpolynomial *qp,
7213 __isl_take isl_set *context);
7214 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
7215 __isl_take isl_qpolynomial *qp,
7216 __isl_take isl_set *context);
7217 __isl_give isl_qpolynomial_fold *
7218 isl_qpolynomial_fold_gist_params(
7219 __isl_take isl_qpolynomial_fold *fold,
7220 __isl_take isl_set *context);
7221 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7222 __isl_take isl_qpolynomial_fold *fold,
7223 __isl_take isl_set *context);
7224 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7225 __isl_take isl_pw_qpolynomial *pwqp,
7226 __isl_take isl_set *context);
7227 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7228 __isl_take isl_pw_qpolynomial *pwqp,
7229 __isl_take isl_set *context);
7230 __isl_give isl_pw_qpolynomial_fold *
7231 isl_pw_qpolynomial_fold_gist(
7232 __isl_take isl_pw_qpolynomial_fold *pwf,
7233 __isl_take isl_set *context);
7234 __isl_give isl_pw_qpolynomial_fold *
7235 isl_pw_qpolynomial_fold_gist_params(
7236 __isl_take isl_pw_qpolynomial_fold *pwf,
7237 __isl_take isl_set *context);
7238 __isl_give isl_union_pw_qpolynomial *
7239 isl_union_pw_qpolynomial_gist_params(
7240 __isl_take isl_union_pw_qpolynomial *upwqp,
7241 __isl_take isl_set *context);
7242 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7243 __isl_take isl_union_pw_qpolynomial *upwqp,
7244 __isl_take isl_union_set *context);
7245 __isl_give isl_union_pw_qpolynomial_fold *
7246 isl_union_pw_qpolynomial_fold_gist(
7247 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7248 __isl_take isl_union_set *context);
7249 __isl_give isl_union_pw_qpolynomial_fold *
7250 isl_union_pw_qpolynomial_fold_gist_params(
7251 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7252 __isl_take isl_set *context);
7254 =item * Binary Arithmetic Operations
7256 #include <isl/set.h>
7257 __isl_give isl_set *isl_set_sum(
7258 __isl_take isl_set *set1,
7259 __isl_take isl_set *set2);
7260 #include <isl/map.h>
7261 __isl_give isl_map *isl_map_sum(
7262 __isl_take isl_map *map1,
7263 __isl_take isl_map *map2);
7265 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7266 i.e., the set containing the sums of pairs of elements from
7267 C<set1> and C<set2>.
7268 The domain of the result of C<isl_map_sum> is the intersection
7269 of the domains of its two arguments. The corresponding range
7270 elements are the sums of the corresponding range elements
7271 in the two arguments.
7273 #include <isl/val.h>
7274 __isl_give isl_multi_val *isl_multi_val_add(
7275 __isl_take isl_multi_val *mv1,
7276 __isl_take isl_multi_val *mv2);
7277 __isl_give isl_multi_val *isl_multi_val_sub(
7278 __isl_take isl_multi_val *mv1,
7279 __isl_take isl_multi_val *mv2);
7281 #include <isl/aff.h>
7282 __isl_give isl_aff *isl_aff_add(
7283 __isl_take isl_aff *aff1,
7284 __isl_take isl_aff *aff2);
7285 __isl_give isl_multi_aff *isl_multi_aff_add(
7286 __isl_take isl_multi_aff *maff1,
7287 __isl_take isl_multi_aff *maff2);
7288 __isl_give isl_pw_aff *isl_pw_aff_add(
7289 __isl_take isl_pw_aff *pwaff1,
7290 __isl_take isl_pw_aff *pwaff2);
7291 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7292 __isl_take isl_multi_pw_aff *mpa1,
7293 __isl_take isl_multi_pw_aff *mpa2);
7294 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7295 __isl_take isl_pw_multi_aff *pma1,
7296 __isl_take isl_pw_multi_aff *pma2);
7297 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7298 __isl_take isl_union_pw_aff *upa1,
7299 __isl_take isl_union_pw_aff *upa2);
7300 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7301 __isl_take isl_union_pw_multi_aff *upma1,
7302 __isl_take isl_union_pw_multi_aff *upma2);
7303 __isl_give isl_multi_union_pw_aff *
7304 isl_multi_union_pw_aff_add(
7305 __isl_take isl_multi_union_pw_aff *mupa1,
7306 __isl_take isl_multi_union_pw_aff *mupa2);
7307 __isl_give isl_pw_aff *isl_pw_aff_min(
7308 __isl_take isl_pw_aff *pwaff1,
7309 __isl_take isl_pw_aff *pwaff2);
7310 __isl_give isl_pw_aff *isl_pw_aff_max(
7311 __isl_take isl_pw_aff *pwaff1,
7312 __isl_take isl_pw_aff *pwaff2);
7313 __isl_give isl_aff *isl_aff_sub(
7314 __isl_take isl_aff *aff1,
7315 __isl_take isl_aff *aff2);
7316 __isl_give isl_multi_aff *isl_multi_aff_sub(
7317 __isl_take isl_multi_aff *ma1,
7318 __isl_take isl_multi_aff *ma2);
7319 __isl_give isl_pw_aff *isl_pw_aff_sub(
7320 __isl_take isl_pw_aff *pwaff1,
7321 __isl_take isl_pw_aff *pwaff2);
7322 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7323 __isl_take isl_multi_pw_aff *mpa1,
7324 __isl_take isl_multi_pw_aff *mpa2);
7325 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7326 __isl_take isl_pw_multi_aff *pma1,
7327 __isl_take isl_pw_multi_aff *pma2);
7328 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7329 __isl_take isl_union_pw_aff *upa1,
7330 __isl_take isl_union_pw_aff *upa2);
7331 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7332 __isl_take isl_union_pw_multi_aff *upma1,
7333 __isl_take isl_union_pw_multi_aff *upma2);
7334 __isl_give isl_multi_union_pw_aff *
7335 isl_multi_union_pw_aff_sub(
7336 __isl_take isl_multi_union_pw_aff *mupa1,
7337 __isl_take isl_multi_union_pw_aff *mupa2);
7339 C<isl_aff_sub> subtracts the second argument from the first.
7341 #include <isl/polynomial.h>
7342 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7343 __isl_take isl_qpolynomial *qp1,
7344 __isl_take isl_qpolynomial *qp2);
7345 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7346 __isl_take isl_pw_qpolynomial *pwqp1,
7347 __isl_take isl_pw_qpolynomial *pwqp2);
7348 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7349 __isl_take isl_pw_qpolynomial *pwqp1,
7350 __isl_take isl_pw_qpolynomial *pwqp2);
7351 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7352 __isl_take isl_pw_qpolynomial_fold *pwf1,
7353 __isl_take isl_pw_qpolynomial_fold *pwf2);
7354 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7355 __isl_take isl_union_pw_qpolynomial *upwqp1,
7356 __isl_take isl_union_pw_qpolynomial *upwqp2);
7357 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7358 __isl_take isl_qpolynomial *qp1,
7359 __isl_take isl_qpolynomial *qp2);
7360 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7361 __isl_take isl_pw_qpolynomial *pwqp1,
7362 __isl_take isl_pw_qpolynomial *pwqp2);
7363 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7364 __isl_take isl_union_pw_qpolynomial *upwqp1,
7365 __isl_take isl_union_pw_qpolynomial *upwqp2);
7366 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7367 __isl_take isl_pw_qpolynomial_fold *pwf1,
7368 __isl_take isl_pw_qpolynomial_fold *pwf2);
7369 __isl_give isl_union_pw_qpolynomial_fold *
7370 isl_union_pw_qpolynomial_fold_fold(
7371 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7372 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7374 #include <isl/aff.h>
7375 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7376 __isl_take isl_pw_aff *pwaff1,
7377 __isl_take isl_pw_aff *pwaff2);
7378 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7379 __isl_take isl_pw_multi_aff *pma1,
7380 __isl_take isl_pw_multi_aff *pma2);
7381 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7382 __isl_take isl_union_pw_aff *upa1,
7383 __isl_take isl_union_pw_aff *upa2);
7384 __isl_give isl_union_pw_multi_aff *
7385 isl_union_pw_multi_aff_union_add(
7386 __isl_take isl_union_pw_multi_aff *upma1,
7387 __isl_take isl_union_pw_multi_aff *upma2);
7388 __isl_give isl_multi_union_pw_aff *
7389 isl_multi_union_pw_aff_union_add(
7390 __isl_take isl_multi_union_pw_aff *mupa1,
7391 __isl_take isl_multi_union_pw_aff *mupa2);
7392 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7393 __isl_take isl_pw_aff *pwaff1,
7394 __isl_take isl_pw_aff *pwaff2);
7395 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7396 __isl_take isl_pw_aff *pwaff1,
7397 __isl_take isl_pw_aff *pwaff2);
7399 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7400 expression with a domain that is the union of those of C<pwaff1> and
7401 C<pwaff2> and such that on each cell, the quasi-affine expression is
7402 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7403 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7404 associated expression is the defined one.
7405 This in contrast to the C<isl_pw_aff_max> function, which is
7406 only defined on the shared definition domain of the arguments.
7408 #include <isl/val.h>
7409 __isl_give isl_multi_val *isl_multi_val_add_val(
7410 __isl_take isl_multi_val *mv,
7411 __isl_take isl_val *v);
7412 __isl_give isl_multi_val *isl_multi_val_mod_val(
7413 __isl_take isl_multi_val *mv,
7414 __isl_take isl_val *v);
7415 __isl_give isl_multi_val *isl_multi_val_scale_val(
7416 __isl_take isl_multi_val *mv,
7417 __isl_take isl_val *v);
7418 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7419 __isl_take isl_multi_val *mv,
7420 __isl_take isl_val *v);
7422 #include <isl/aff.h>
7423 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7424 __isl_take isl_val *mod);
7425 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7426 __isl_take isl_pw_aff *pa,
7427 __isl_take isl_val *mod);
7428 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7429 __isl_take isl_union_pw_aff *upa,
7430 __isl_take isl_val *f);
7431 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7432 __isl_take isl_val *v);
7433 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7434 __isl_take isl_multi_aff *ma,
7435 __isl_take isl_val *v);
7436 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7437 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7438 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7439 __isl_take isl_multi_pw_aff *mpa,
7440 __isl_take isl_val *v);
7441 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7442 __isl_take isl_pw_multi_aff *pma,
7443 __isl_take isl_val *v);
7444 __isl_give isl_union_pw_multi_aff *
7445 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7446 __isl_take isl_union_pw_aff *upa,
7447 __isl_take isl_val *f);
7448 isl_union_pw_multi_aff_scale_val(
7449 __isl_take isl_union_pw_multi_aff *upma,
7450 __isl_take isl_val *val);
7451 __isl_give isl_multi_union_pw_aff *
7452 isl_multi_union_pw_aff_scale_val(
7453 __isl_take isl_multi_union_pw_aff *mupa,
7454 __isl_take isl_val *v);
7455 __isl_give isl_aff *isl_aff_scale_down_ui(
7456 __isl_take isl_aff *aff, unsigned f);
7457 __isl_give isl_aff *isl_aff_scale_down_val(
7458 __isl_take isl_aff *aff, __isl_take isl_val *v);
7459 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7460 __isl_take isl_multi_aff *ma,
7461 __isl_take isl_val *v);
7462 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7463 __isl_take isl_pw_aff *pa,
7464 __isl_take isl_val *f);
7465 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7466 __isl_take isl_multi_pw_aff *mpa,
7467 __isl_take isl_val *v);
7468 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7469 __isl_take isl_pw_multi_aff *pma,
7470 __isl_take isl_val *v);
7471 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7472 __isl_take isl_union_pw_aff *upa,
7473 __isl_take isl_val *v);
7474 __isl_give isl_union_pw_multi_aff *
7475 isl_union_pw_multi_aff_scale_down_val(
7476 __isl_take isl_union_pw_multi_aff *upma,
7477 __isl_take isl_val *val);
7478 __isl_give isl_multi_union_pw_aff *
7479 isl_multi_union_pw_aff_scale_down_val(
7480 __isl_take isl_multi_union_pw_aff *mupa,
7481 __isl_take isl_val *v);
7483 #include <isl/polynomial.h>
7484 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7485 __isl_take isl_qpolynomial *qp,
7486 __isl_take isl_val *v);
7487 __isl_give isl_qpolynomial_fold *
7488 isl_qpolynomial_fold_scale_val(
7489 __isl_take isl_qpolynomial_fold *fold,
7490 __isl_take isl_val *v);
7491 __isl_give isl_pw_qpolynomial *
7492 isl_pw_qpolynomial_scale_val(
7493 __isl_take isl_pw_qpolynomial *pwqp,
7494 __isl_take isl_val *v);
7495 __isl_give isl_pw_qpolynomial_fold *
7496 isl_pw_qpolynomial_fold_scale_val(
7497 __isl_take isl_pw_qpolynomial_fold *pwf,
7498 __isl_take isl_val *v);
7499 __isl_give isl_union_pw_qpolynomial *
7500 isl_union_pw_qpolynomial_scale_val(
7501 __isl_take isl_union_pw_qpolynomial *upwqp,
7502 __isl_take isl_val *v);
7503 __isl_give isl_union_pw_qpolynomial_fold *
7504 isl_union_pw_qpolynomial_fold_scale_val(
7505 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7506 __isl_take isl_val *v);
7507 __isl_give isl_qpolynomial *
7508 isl_qpolynomial_scale_down_val(
7509 __isl_take isl_qpolynomial *qp,
7510 __isl_take isl_val *v);
7511 __isl_give isl_qpolynomial_fold *
7512 isl_qpolynomial_fold_scale_down_val(
7513 __isl_take isl_qpolynomial_fold *fold,
7514 __isl_take isl_val *v);
7515 __isl_give isl_pw_qpolynomial *
7516 isl_pw_qpolynomial_scale_down_val(
7517 __isl_take isl_pw_qpolynomial *pwqp,
7518 __isl_take isl_val *v);
7519 __isl_give isl_pw_qpolynomial_fold *
7520 isl_pw_qpolynomial_fold_scale_down_val(
7521 __isl_take isl_pw_qpolynomial_fold *pwf,
7522 __isl_take isl_val *v);
7523 __isl_give isl_union_pw_qpolynomial *
7524 isl_union_pw_qpolynomial_scale_down_val(
7525 __isl_take isl_union_pw_qpolynomial *upwqp,
7526 __isl_take isl_val *v);
7527 __isl_give isl_union_pw_qpolynomial_fold *
7528 isl_union_pw_qpolynomial_fold_scale_down_val(
7529 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7530 __isl_take isl_val *v);
7532 #include <isl/val.h>
7533 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7534 __isl_take isl_multi_val *mv1,
7535 __isl_take isl_multi_val *mv2);
7536 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7537 __isl_take isl_multi_val *mv1,
7538 __isl_take isl_multi_val *mv2);
7539 __isl_give isl_multi_val *
7540 isl_multi_val_scale_down_multi_val(
7541 __isl_take isl_multi_val *mv1,
7542 __isl_take isl_multi_val *mv2);
7544 #include <isl/aff.h>
7545 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7546 __isl_take isl_multi_aff *ma,
7547 __isl_take isl_multi_val *mv);
7548 __isl_give isl_multi_union_pw_aff *
7549 isl_multi_union_pw_aff_mod_multi_val(
7550 __isl_take isl_multi_union_pw_aff *upma,
7551 __isl_take isl_multi_val *mv);
7552 __isl_give isl_multi_pw_aff *
7553 isl_multi_pw_aff_mod_multi_val(
7554 __isl_take isl_multi_pw_aff *mpa,
7555 __isl_take isl_multi_val *mv);
7556 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7557 __isl_take isl_multi_aff *ma,
7558 __isl_take isl_multi_val *mv);
7559 __isl_give isl_pw_multi_aff *
7560 isl_pw_multi_aff_scale_multi_val(
7561 __isl_take isl_pw_multi_aff *pma,
7562 __isl_take isl_multi_val *mv);
7563 __isl_give isl_multi_pw_aff *
7564 isl_multi_pw_aff_scale_multi_val(
7565 __isl_take isl_multi_pw_aff *mpa,
7566 __isl_take isl_multi_val *mv);
7567 __isl_give isl_multi_union_pw_aff *
7568 isl_multi_union_pw_aff_scale_multi_val(
7569 __isl_take isl_multi_union_pw_aff *mupa,
7570 __isl_take isl_multi_val *mv);
7571 __isl_give isl_union_pw_multi_aff *
7572 isl_union_pw_multi_aff_scale_multi_val(
7573 __isl_take isl_union_pw_multi_aff *upma,
7574 __isl_take isl_multi_val *mv);
7575 __isl_give isl_multi_aff *
7576 isl_multi_aff_scale_down_multi_val(
7577 __isl_take isl_multi_aff *ma,
7578 __isl_take isl_multi_val *mv);
7579 __isl_give isl_multi_pw_aff *
7580 isl_multi_pw_aff_scale_down_multi_val(
7581 __isl_take isl_multi_pw_aff *mpa,
7582 __isl_take isl_multi_val *mv);
7583 __isl_give isl_multi_union_pw_aff *
7584 isl_multi_union_pw_aff_scale_down_multi_val(
7585 __isl_take isl_multi_union_pw_aff *mupa,
7586 __isl_take isl_multi_val *mv);
7588 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7589 by the corresponding elements of C<mv>.
7591 #include <isl/aff.h>
7592 __isl_give isl_aff *isl_aff_mul(
7593 __isl_take isl_aff *aff1,
7594 __isl_take isl_aff *aff2);
7595 __isl_give isl_aff *isl_aff_div(
7596 __isl_take isl_aff *aff1,
7597 __isl_take isl_aff *aff2);
7598 __isl_give isl_pw_aff *isl_pw_aff_mul(
7599 __isl_take isl_pw_aff *pwaff1,
7600 __isl_take isl_pw_aff *pwaff2);
7601 __isl_give isl_pw_aff *isl_pw_aff_div(
7602 __isl_take isl_pw_aff *pa1,
7603 __isl_take isl_pw_aff *pa2);
7604 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7605 __isl_take isl_pw_aff *pa1,
7606 __isl_take isl_pw_aff *pa2);
7607 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7608 __isl_take isl_pw_aff *pa1,
7609 __isl_take isl_pw_aff *pa2);
7611 When multiplying two affine expressions, at least one of the two needs
7612 to be a constant. Similarly, when dividing an affine expression by another,
7613 the second expression needs to be a constant.
7614 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7615 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7618 #include <isl/polynomial.h>
7619 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7620 __isl_take isl_qpolynomial *qp1,
7621 __isl_take isl_qpolynomial *qp2);
7622 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7623 __isl_take isl_pw_qpolynomial *pwqp1,
7624 __isl_take isl_pw_qpolynomial *pwqp2);
7625 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7626 __isl_take isl_union_pw_qpolynomial *upwqp1,
7627 __isl_take isl_union_pw_qpolynomial *upwqp2);
7631 =head3 Lexicographic Optimization
7633 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7634 the following functions
7635 compute a set that contains the lexicographic minimum or maximum
7636 of the elements in C<set> (or C<bset>) for those values of the parameters
7637 that satisfy C<dom>.
7638 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7639 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7641 In other words, the union of the parameter values
7642 for which the result is non-empty and of C<*empty>
7645 #include <isl/set.h>
7646 __isl_give isl_set *isl_basic_set_partial_lexmin(
7647 __isl_take isl_basic_set *bset,
7648 __isl_take isl_basic_set *dom,
7649 __isl_give isl_set **empty);
7650 __isl_give isl_set *isl_basic_set_partial_lexmax(
7651 __isl_take isl_basic_set *bset,
7652 __isl_take isl_basic_set *dom,
7653 __isl_give isl_set **empty);
7654 __isl_give isl_set *isl_set_partial_lexmin(
7655 __isl_take isl_set *set, __isl_take isl_set *dom,
7656 __isl_give isl_set **empty);
7657 __isl_give isl_set *isl_set_partial_lexmax(
7658 __isl_take isl_set *set, __isl_take isl_set *dom,
7659 __isl_give isl_set **empty);
7661 Given a (basic) set C<set> (or C<bset>), the following functions simply
7662 return a set containing the lexicographic minimum or maximum
7663 of the elements in C<set> (or C<bset>).
7664 In case of union sets, the optimum is computed per space.
7666 #include <isl/set.h>
7667 __isl_give isl_set *isl_basic_set_lexmin(
7668 __isl_take isl_basic_set *bset);
7669 __isl_give isl_set *isl_basic_set_lexmax(
7670 __isl_take isl_basic_set *bset);
7671 __isl_give isl_set *isl_set_lexmin(
7672 __isl_take isl_set *set);
7673 __isl_give isl_set *isl_set_lexmax(
7674 __isl_take isl_set *set);
7675 __isl_give isl_union_set *isl_union_set_lexmin(
7676 __isl_take isl_union_set *uset);
7677 __isl_give isl_union_set *isl_union_set_lexmax(
7678 __isl_take isl_union_set *uset);
7680 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7681 the following functions
7682 compute a relation that maps each element of C<dom>
7683 to the single lexicographic minimum or maximum
7684 of the elements that are associated to that same
7685 element in C<map> (or C<bmap>).
7686 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7687 that contains the elements in C<dom> that do not map
7688 to any elements in C<map> (or C<bmap>).
7689 In other words, the union of the domain of the result and of C<*empty>
7692 #include <isl/map.h>
7693 __isl_give isl_map *isl_basic_map_partial_lexmax(
7694 __isl_take isl_basic_map *bmap,
7695 __isl_take isl_basic_set *dom,
7696 __isl_give isl_set **empty);
7697 __isl_give isl_map *isl_basic_map_partial_lexmin(
7698 __isl_take isl_basic_map *bmap,
7699 __isl_take isl_basic_set *dom,
7700 __isl_give isl_set **empty);
7701 __isl_give isl_map *isl_map_partial_lexmax(
7702 __isl_take isl_map *map, __isl_take isl_set *dom,
7703 __isl_give isl_set **empty);
7704 __isl_give isl_map *isl_map_partial_lexmin(
7705 __isl_take isl_map *map, __isl_take isl_set *dom,
7706 __isl_give isl_set **empty);
7708 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7709 return a map mapping each element in the domain of
7710 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7711 of all elements associated to that element.
7712 In case of union relations, the optimum is computed per space.
7714 #include <isl/map.h>
7715 __isl_give isl_map *isl_basic_map_lexmin(
7716 __isl_take isl_basic_map *bmap);
7717 __isl_give isl_map *isl_basic_map_lexmax(
7718 __isl_take isl_basic_map *bmap);
7719 __isl_give isl_map *isl_map_lexmin(
7720 __isl_take isl_map *map);
7721 __isl_give isl_map *isl_map_lexmax(
7722 __isl_take isl_map *map);
7723 __isl_give isl_union_map *isl_union_map_lexmin(
7724 __isl_take isl_union_map *umap);
7725 __isl_give isl_union_map *isl_union_map_lexmax(
7726 __isl_take isl_union_map *umap);
7728 The following functions return their result in the form of
7729 a piecewise multi-affine expression,
7730 but are otherwise equivalent to the corresponding functions
7731 returning a basic set or relation.
7733 #include <isl/set.h>
7734 __isl_give isl_pw_multi_aff *
7735 isl_basic_set_partial_lexmin_pw_multi_aff(
7736 __isl_take isl_basic_set *bset,
7737 __isl_take isl_basic_set *dom,
7738 __isl_give isl_set **empty);
7739 __isl_give isl_pw_multi_aff *
7740 isl_basic_set_partial_lexmax_pw_multi_aff(
7741 __isl_take isl_basic_set *bset,
7742 __isl_take isl_basic_set *dom,
7743 __isl_give isl_set **empty);
7744 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7745 __isl_take isl_set *set);
7746 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7747 __isl_take isl_set *set);
7749 #include <isl/map.h>
7750 __isl_give isl_pw_multi_aff *
7751 isl_basic_map_lexmin_pw_multi_aff(
7752 __isl_take isl_basic_map *bmap);
7753 __isl_give isl_pw_multi_aff *
7754 isl_basic_map_partial_lexmin_pw_multi_aff(
7755 __isl_take isl_basic_map *bmap,
7756 __isl_take isl_basic_set *dom,
7757 __isl_give isl_set **empty);
7758 __isl_give isl_pw_multi_aff *
7759 isl_basic_map_partial_lexmax_pw_multi_aff(
7760 __isl_take isl_basic_map *bmap,
7761 __isl_take isl_basic_set *dom,
7762 __isl_give isl_set **empty);
7763 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7764 __isl_take isl_map *map);
7765 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7766 __isl_take isl_map *map);
7768 The following functions return the lexicographic minimum or maximum
7769 on the shared domain of the inputs and the single defined function
7770 on those parts of the domain where only a single function is defined.
7772 #include <isl/aff.h>
7773 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7774 __isl_take isl_pw_multi_aff *pma1,
7775 __isl_take isl_pw_multi_aff *pma2);
7776 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7777 __isl_take isl_pw_multi_aff *pma1,
7778 __isl_take isl_pw_multi_aff *pma2);
7780 If the input to a lexicographic optimization problem has
7781 multiple constraints with the same coefficients for the optimized
7782 variables, then, by default, this symmetry is exploited by
7783 replacing those constraints by a single constraint with
7784 an abstract bound, which is in turn bounded by the corresponding terms
7785 in the original constraints.
7786 Without this optimization, the solver would typically consider
7787 all possible orderings of those original bounds, resulting in a needless
7788 decomposition of the domain.
7789 However, the optimization can also result in slowdowns since
7790 an extra parameter is introduced that may get used in additional
7792 The following option determines whether symmetry detection is applied
7793 during lexicographic optimization.
7795 #include <isl/options.h>
7796 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7798 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7802 See also \autoref{s:offline}.
7806 =head2 Ternary Operations
7808 #include <isl/aff.h>
7809 __isl_give isl_pw_aff *isl_pw_aff_cond(
7810 __isl_take isl_pw_aff *cond,
7811 __isl_take isl_pw_aff *pwaff_true,
7812 __isl_take isl_pw_aff *pwaff_false);
7814 The function C<isl_pw_aff_cond> performs a conditional operator
7815 and returns an expression that is equal to C<pwaff_true>
7816 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7817 where C<cond> is zero.
7821 Lists are defined over several element types, including
7822 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
7823 C<isl_union_pw_aff>,
7824 C<isl_union_pw_multi_aff>,
7825 C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
7827 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7828 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7829 Here we take lists of C<isl_set>s as an example.
7830 Lists can be created, copied, modified and freed using the following functions.
7832 #include <isl/set.h>
7833 __isl_give isl_set_list *isl_set_list_from_set(
7834 __isl_take isl_set *el);
7835 __isl_give isl_set_list *isl_set_list_alloc(
7836 isl_ctx *ctx, int n);
7837 __isl_give isl_set_list *isl_set_list_copy(
7838 __isl_keep isl_set_list *list);
7839 __isl_give isl_set_list *isl_set_list_insert(
7840 __isl_take isl_set_list *list, unsigned pos,
7841 __isl_take isl_set *el);
7842 __isl_give isl_set_list *isl_set_list_add(
7843 __isl_take isl_set_list *list,
7844 __isl_take isl_set *el);
7845 __isl_give isl_set_list *isl_set_list_drop(
7846 __isl_take isl_set_list *list,
7847 unsigned first, unsigned n);
7848 __isl_give isl_set_list *isl_set_list_set_set(
7849 __isl_take isl_set_list *list, int index,
7850 __isl_take isl_set *set);
7851 __isl_give isl_set_list *isl_set_list_concat(
7852 __isl_take isl_set_list *list1,
7853 __isl_take isl_set_list *list2);
7854 __isl_give isl_set_list *isl_set_list_map(
7855 __isl_take isl_set_list *list,
7856 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7859 __isl_give isl_set_list *isl_set_list_sort(
7860 __isl_take isl_set_list *list,
7861 int (*cmp)(__isl_keep isl_set *a,
7862 __isl_keep isl_set *b, void *user),
7864 __isl_null isl_set_list *isl_set_list_free(
7865 __isl_take isl_set_list *list);
7867 C<isl_set_list_alloc> creates an empty list with an initial capacity
7868 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7869 add elements to a list, increasing its capacity as needed.
7870 C<isl_set_list_from_set> creates a list with a single element.
7872 Lists can be inspected using the following functions.
7874 #include <isl/set.h>
7875 int isl_set_list_size(__isl_keep isl_set_list *list);
7876 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7877 __isl_give isl_set *isl_set_list_get_at(
7878 __isl_keep isl_set_list *list, int index);
7879 __isl_give isl_set *isl_set_list_get_set(
7880 __isl_keep isl_set_list *list, int index);
7881 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7882 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7884 isl_stat isl_set_list_foreach_scc(
7885 __isl_keep isl_set_list *list,
7886 isl_bool (*follows)(__isl_keep isl_set *a,
7887 __isl_keep isl_set *b, void *user),
7889 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7892 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
7894 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
7895 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7896 strongly connected components of the graph with as vertices the elements
7897 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7898 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7899 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7901 Lists can be printed using
7903 #include <isl/set.h>
7904 __isl_give isl_printer *isl_printer_print_set_list(
7905 __isl_take isl_printer *p,
7906 __isl_keep isl_set_list *list);
7908 =head2 Associative arrays
7910 Associative arrays map isl objects of a specific type to isl objects
7911 of some (other) specific type. They are defined for several pairs
7912 of types, including (C<isl_map>, C<isl_basic_set>),
7913 (C<isl_id>, C<isl_ast_expr>),
7914 (C<isl_id>, C<isl_id>) and
7915 (C<isl_id>, C<isl_pw_aff>).
7916 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7919 Associative arrays can be created, copied and freed using
7920 the following functions.
7922 #include <isl/id_to_ast_expr.h>
7923 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7924 isl_ctx *ctx, int min_size);
7925 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7926 __isl_keep isl_id_to_ast_expr *id2expr);
7927 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7928 __isl_take isl_id_to_ast_expr *id2expr);
7930 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7931 to specify the expected size of the associative array.
7932 The associative array will be grown automatically as needed.
7934 Associative arrays can be inspected using the following functions.
7936 #include <isl/id_to_ast_expr.h>
7937 __isl_give isl_maybe_isl_ast_expr
7938 isl_id_to_ast_expr_try_get(
7939 __isl_keep isl_id_to_ast_expr *id2expr,
7940 __isl_keep isl_id *key);
7941 isl_bool isl_id_to_ast_expr_has(
7942 __isl_keep isl_id_to_ast_expr *id2expr,
7943 __isl_keep isl_id *key);
7944 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7945 __isl_keep isl_id_to_ast_expr *id2expr,
7946 __isl_take isl_id *key);
7947 isl_stat isl_id_to_ast_expr_foreach(
7948 __isl_keep isl_id_to_ast_expr *id2expr,
7949 isl_stat (*fn)(__isl_take isl_id *key,
7950 __isl_take isl_ast_expr *val, void *user),
7953 The function C<isl_id_to_ast_expr_try_get> returns a structure
7954 containing two elements, C<valid> and C<value>.
7955 If there is a value associated to the key, then C<valid>
7956 is set to C<isl_bool_true> and C<value> contains a copy of
7957 the associated value. Otherwise C<value> is C<NULL> and
7958 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7959 on whether some error has occurred or there simply is no associated value.
7960 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7961 in the structure and
7962 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7964 Associative arrays can be modified using the following functions.
7966 #include <isl/id_to_ast_expr.h>
7967 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7968 __isl_take isl_id_to_ast_expr *id2expr,
7969 __isl_take isl_id *key,
7970 __isl_take isl_ast_expr *val);
7971 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7972 __isl_take isl_id_to_ast_expr *id2expr,
7973 __isl_take isl_id *key);
7975 Associative arrays can be printed using the following function.
7977 #include <isl/id_to_ast_expr.h>
7978 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7979 __isl_take isl_printer *p,
7980 __isl_keep isl_id_to_ast_expr *id2expr);
7984 Vectors can be created, copied and freed using the following functions.
7986 #include <isl/vec.h>
7987 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7989 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
7991 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7992 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7994 Note that the elements of a vector created by C<isl_vec_alloc>
7995 may have arbitrary values.
7996 A vector created by C<isl_vec_zero> has elements with value zero.
7997 The elements can be changed and inspected using the following functions.
7999 int isl_vec_size(__isl_keep isl_vec *vec);
8000 __isl_give isl_val *isl_vec_get_element_val(
8001 __isl_keep isl_vec *vec, int pos);
8002 __isl_give isl_vec *isl_vec_set_element_si(
8003 __isl_take isl_vec *vec, int pos, int v);
8004 __isl_give isl_vec *isl_vec_set_element_val(
8005 __isl_take isl_vec *vec, int pos,
8006 __isl_take isl_val *v);
8007 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
8009 __isl_give isl_vec *isl_vec_set_val(
8010 __isl_take isl_vec *vec, __isl_take isl_val *v);
8011 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
8012 __isl_keep isl_vec *vec2, int pos);
8014 C<isl_vec_get_element> will return a negative value if anything went wrong.
8015 In that case, the value of C<*v> is undefined.
8017 The following function can be used to concatenate two vectors.
8019 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
8020 __isl_take isl_vec *vec2);
8024 Matrices can be created, copied and freed using the following functions.
8026 #include <isl/mat.h>
8027 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
8028 unsigned n_row, unsigned n_col);
8029 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
8030 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
8032 Note that the elements of a newly created matrix may have arbitrary values.
8033 The elements can be changed and inspected using the following functions.
8035 int isl_mat_rows(__isl_keep isl_mat *mat);
8036 int isl_mat_cols(__isl_keep isl_mat *mat);
8037 __isl_give isl_val *isl_mat_get_element_val(
8038 __isl_keep isl_mat *mat, int row, int col);
8039 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
8040 int row, int col, int v);
8041 __isl_give isl_mat *isl_mat_set_element_val(
8042 __isl_take isl_mat *mat, int row, int col,
8043 __isl_take isl_val *v);
8045 The following function computes the rank of a matrix.
8046 The return value may be -1 if some error occurred.
8048 #include <isl/mat.h>
8049 int isl_mat_rank(__isl_keep isl_mat *mat);
8051 The following function can be used to compute the (right) inverse
8052 of a matrix, i.e., a matrix such that the product of the original
8053 and the inverse (in that order) is a multiple of the identity matrix.
8054 The input matrix is assumed to be of full row-rank.
8056 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
8058 The following function can be used to compute the (right) kernel
8059 (or null space) of a matrix, i.e., a matrix such that the product of
8060 the original and the kernel (in that order) is the zero matrix.
8062 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
8064 The following function computes a basis for the space spanned
8065 by the rows of a matrix.
8067 __isl_give isl_mat *isl_mat_row_basis(
8068 __isl_take isl_mat *mat);
8070 The following function computes rows that extend a basis of C<mat1>
8071 to a basis that also covers C<mat2>.
8073 __isl_give isl_mat *isl_mat_row_basis_extension(
8074 __isl_take isl_mat *mat1,
8075 __isl_take isl_mat *mat2);
8077 The following function checks whether there is no linear dependence
8078 among the combined rows of "mat1" and "mat2" that is not already present
8079 in "mat1" or "mat2" individually.
8080 If "mat1" and "mat2" have linearly independent rows by themselves,
8081 then this means that there is no linear dependence among all rows together.
8083 isl_bool isl_mat_has_linearly_independent_rows(
8084 __isl_keep isl_mat *mat1,
8085 __isl_keep isl_mat *mat2);
8087 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
8089 The following functions determine
8090 an upper or lower bound on a quasipolynomial over its domain.
8092 __isl_give isl_pw_qpolynomial_fold *
8093 isl_pw_qpolynomial_bound(
8094 __isl_take isl_pw_qpolynomial *pwqp,
8095 enum isl_fold type, int *tight);
8097 __isl_give isl_union_pw_qpolynomial_fold *
8098 isl_union_pw_qpolynomial_bound(
8099 __isl_take isl_union_pw_qpolynomial *upwqp,
8100 enum isl_fold type, int *tight);
8102 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
8103 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
8104 is the returned bound is known be tight, i.e., for each value
8105 of the parameters there is at least
8106 one element in the domain that reaches the bound.
8107 If the domain of C<pwqp> is not wrapping, then the bound is computed
8108 over all elements in that domain and the result has a purely parametric
8109 domain. If the domain of C<pwqp> is wrapping, then the bound is
8110 computed over the range of the wrapped relation. The domain of the
8111 wrapped relation becomes the domain of the result.
8113 =head2 Parametric Vertex Enumeration
8115 The parametric vertex enumeration described in this section
8116 is mainly intended to be used internally and by the C<barvinok>
8119 #include <isl/vertices.h>
8120 __isl_give isl_vertices *isl_basic_set_compute_vertices(
8121 __isl_keep isl_basic_set *bset);
8123 The function C<isl_basic_set_compute_vertices> performs the
8124 actual computation of the parametric vertices and the chamber
8125 decomposition and stores the result in an C<isl_vertices> object.
8126 This information can be queried by either iterating over all
8127 the vertices or iterating over all the chambers or cells
8128 and then iterating over all vertices that are active on the chamber.
8130 isl_stat isl_vertices_foreach_vertex(
8131 __isl_keep isl_vertices *vertices,
8132 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8133 void *user), void *user);
8135 isl_stat isl_vertices_foreach_cell(
8136 __isl_keep isl_vertices *vertices,
8137 isl_stat (*fn)(__isl_take isl_cell *cell,
8138 void *user), void *user);
8139 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
8140 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8141 void *user), void *user);
8143 Other operations that can be performed on an C<isl_vertices> object are
8146 int isl_vertices_get_n_vertices(
8147 __isl_keep isl_vertices *vertices);
8148 __isl_null isl_vertices *isl_vertices_free(
8149 __isl_take isl_vertices *vertices);
8151 Vertices can be inspected and destroyed using the following functions.
8153 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
8154 __isl_give isl_basic_set *isl_vertex_get_domain(
8155 __isl_keep isl_vertex *vertex);
8156 __isl_give isl_multi_aff *isl_vertex_get_expr(
8157 __isl_keep isl_vertex *vertex);
8158 void isl_vertex_free(__isl_take isl_vertex *vertex);
8160 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
8161 describing the vertex in terms of the parameters,
8162 while C<isl_vertex_get_domain> returns the activity domain
8165 Chambers can be inspected and destroyed using the following functions.
8167 __isl_give isl_basic_set *isl_cell_get_domain(
8168 __isl_keep isl_cell *cell);
8169 void isl_cell_free(__isl_take isl_cell *cell);
8171 =head1 Polyhedral Compilation Library
8173 This section collects functionality in C<isl> that has been specifically
8174 designed for use during polyhedral compilation.
8176 =head2 Schedule Trees
8178 A schedule tree is a structured representation of a schedule,
8179 assigning a relative order to a set of domain elements.
8180 The relative order expressed by the schedule tree is
8181 defined recursively. In particular, the order between
8182 two domain elements is determined by the node that is closest
8183 to the root that refers to both elements and that orders them apart.
8184 Each node in the tree is of one of several types.
8185 The root node is always of type C<isl_schedule_node_domain>
8186 (or C<isl_schedule_node_extension>)
8187 and it describes the (extra) domain elements to which the schedule applies.
8188 The other types of nodes are as follows.
8192 =item C<isl_schedule_node_band>
8194 A band of schedule dimensions. Each schedule dimension is represented
8195 by a union piecewise quasi-affine expression. If this expression
8196 assigns a different value to two domain elements, while all previous
8197 schedule dimensions in the same band assign them the same value,
8198 then the two domain elements are ordered according to these two
8200 Each expression is required to be total in the domain elements
8201 that reach the band node.
8203 =item C<isl_schedule_node_expansion>
8205 An expansion node maps each of the domain elements that reach the node
8206 to one or more domain elements. The image of this mapping forms
8207 the set of domain elements that reach the child of the expansion node.
8208 The function that maps each of the expanded domain elements
8209 to the original domain element from which it was expanded
8210 is called the contraction.
8212 =item C<isl_schedule_node_filter>
8214 A filter node does not impose any ordering, but rather intersects
8215 the set of domain elements that the current subtree refers to
8216 with a given union set. The subtree of the filter node only
8217 refers to domain elements in the intersection.
8218 A filter node is typically only used as a child of a sequence or
8221 =item C<isl_schedule_node_leaf>
8223 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
8225 =item C<isl_schedule_node_mark>
8227 A mark node can be used to attach any kind of information to a subtree
8228 of the schedule tree.
8230 =item C<isl_schedule_node_sequence>
8232 A sequence node has one or more children, each of which is a filter node.
8233 The filters on these filter nodes form a partition of
8234 the domain elements that the current subtree refers to.
8235 If two domain elements appear in distinct filters then the sequence
8236 node orders them according to the child positions of the corresponding
8239 =item C<isl_schedule_node_set>
8241 A set node is similar to a sequence node, except that
8242 it expresses that domain elements appearing in distinct filters
8243 may have any order. The order of the children of a set node
8244 is therefore also immaterial.
8248 The following node types are only supported by the AST generator.
8252 =item C<isl_schedule_node_context>
8254 The context describes constraints on the parameters and
8255 the schedule dimensions of outer
8256 bands that the AST generator may assume to hold. It is also the only
8257 kind of node that may introduce additional parameters.
8258 The space of the context is that of the flat product of the outer
8259 band nodes. In particular, if there are no outer band nodes, then
8260 this space is the unnamed zero-dimensional space.
8261 Since a context node references the outer band nodes, any tree
8262 containing a context node is considered to be anchored.
8264 =item C<isl_schedule_node_extension>
8266 An extension node instructs the AST generator to add additional
8267 domain elements that need to be scheduled.
8268 The additional domain elements are described by the range of
8269 the extension map in terms of the outer schedule dimensions,
8270 i.e., the flat product of the outer band nodes.
8271 Note that domain elements are added whenever the AST generator
8272 reaches the extension node, meaning that there are still some
8273 active domain elements for which an AST needs to be generated.
8274 The conditions under which some domain elements are still active
8275 may however not be completely described by the outer AST nodes
8276 generated at that point.
8277 Since an extension node references the outer band nodes, any tree
8278 containing an extension node is considered to be anchored.
8280 An extension node may also appear as the root of a schedule tree,
8281 when it is intended to be inserted into another tree
8282 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8283 In this case, the domain of the extension node should
8284 correspond to the flat product of the outer band nodes
8285 in this other schedule tree at the point where the extension tree
8288 =item C<isl_schedule_node_guard>
8290 The guard describes constraints on the parameters and
8291 the schedule dimensions of outer
8292 bands that need to be enforced by the outer nodes
8293 in the generated AST.
8294 That is, the part of the AST that is generated from descendants
8295 of the guard node can assume that these constraints are satisfied.
8296 The space of the guard is that of the flat product of the outer
8297 band nodes. In particular, if there are no outer band nodes, then
8298 this space is the unnamed zero-dimensional space.
8299 Since a guard node references the outer band nodes, any tree
8300 containing a guard node is considered to be anchored.
8304 Except for the C<isl_schedule_node_context> nodes,
8305 none of the nodes may introduce any parameters that were not
8306 already present in the root domain node.
8308 A schedule tree is encapsulated in an C<isl_schedule> object.
8309 The simplest such objects, those with a tree consisting of single domain node,
8310 can be created using the following functions with either an empty
8311 domain or a given domain.
8313 #include <isl/schedule.h>
8314 __isl_give isl_schedule *isl_schedule_empty(
8315 __isl_take isl_space *space);
8316 __isl_give isl_schedule *isl_schedule_from_domain(
8317 __isl_take isl_union_set *domain);
8319 The function C<isl_schedule_constraints_compute_schedule> described
8320 in L</"Scheduling"> can also be used to construct schedules.
8322 C<isl_schedule> objects may be copied and freed using the following functions.
8324 #include <isl/schedule.h>
8325 __isl_give isl_schedule *isl_schedule_copy(
8326 __isl_keep isl_schedule *sched);
8327 __isl_null isl_schedule *isl_schedule_free(
8328 __isl_take isl_schedule *sched);
8330 The following functions checks whether two C<isl_schedule> objects
8331 are obviously the same.
8333 #include <isl/schedule.h>
8334 isl_bool isl_schedule_plain_is_equal(
8335 __isl_keep isl_schedule *schedule1,
8336 __isl_keep isl_schedule *schedule2);
8338 The domain of the schedule, i.e., the domain described by the root node,
8339 can be obtained using the following function.
8341 #include <isl/schedule.h>
8342 __isl_give isl_union_set *isl_schedule_get_domain(
8343 __isl_keep isl_schedule *schedule);
8345 An extra top-level band node (right underneath the domain node) can
8346 be introduced into the schedule using the following function.
8347 The schedule tree is assumed not to have any anchored nodes.
8349 #include <isl/schedule.h>
8350 __isl_give isl_schedule *
8351 isl_schedule_insert_partial_schedule(
8352 __isl_take isl_schedule *schedule,
8353 __isl_take isl_multi_union_pw_aff *partial);
8355 A top-level context node (right underneath the domain node) can
8356 be introduced into the schedule using the following function.
8358 #include <isl/schedule.h>
8359 __isl_give isl_schedule *isl_schedule_insert_context(
8360 __isl_take isl_schedule *schedule,
8361 __isl_take isl_set *context)
8363 A top-level guard node (right underneath the domain node) can
8364 be introduced into the schedule using the following function.
8366 #include <isl/schedule.h>
8367 __isl_give isl_schedule *isl_schedule_insert_guard(
8368 __isl_take isl_schedule *schedule,
8369 __isl_take isl_set *guard)
8371 A schedule that combines two schedules either in the given
8372 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8373 or an C<isl_schedule_node_set> node,
8374 can be created using the following functions.
8376 #include <isl/schedule.h>
8377 __isl_give isl_schedule *isl_schedule_sequence(
8378 __isl_take isl_schedule *schedule1,
8379 __isl_take isl_schedule *schedule2);
8380 __isl_give isl_schedule *isl_schedule_set(
8381 __isl_take isl_schedule *schedule1,
8382 __isl_take isl_schedule *schedule2);
8384 The domains of the two input schedules need to be disjoint.
8386 The following function can be used to restrict the domain
8387 of a schedule with a domain node as root to be a subset of the given union set.
8388 This operation may remove nodes in the tree that have become
8391 #include <isl/schedule.h>
8392 __isl_give isl_schedule *isl_schedule_intersect_domain(
8393 __isl_take isl_schedule *schedule,
8394 __isl_take isl_union_set *domain);
8396 The following function can be used to simplify the domain
8397 of a schedule with a domain node as root with respect to the given
8400 #include <isl/schedule.h>
8401 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8402 __isl_take isl_schedule *schedule,
8403 __isl_take isl_set *context);
8405 The following function resets the user pointers on all parameter
8406 and tuple identifiers referenced by the nodes of the given schedule.
8408 #include <isl/schedule.h>
8409 __isl_give isl_schedule *isl_schedule_reset_user(
8410 __isl_take isl_schedule *schedule);
8412 The following function aligns the parameters of all nodes
8413 in the given schedule to the given space.
8415 #include <isl/schedule.h>
8416 __isl_give isl_schedule *isl_schedule_align_params(
8417 __isl_take isl_schedule *schedule,
8418 __isl_take isl_space *space);
8420 The following function allows the user to plug in a given function
8421 in the iteration domains. The input schedule is not allowed to contain
8422 any expansion nodes.
8424 #include <isl/schedule.h>
8425 __isl_give isl_schedule *
8426 isl_schedule_pullback_union_pw_multi_aff(
8427 __isl_take isl_schedule *schedule,
8428 __isl_take isl_union_pw_multi_aff *upma);
8430 The following function can be used to plug in the schedule C<expansion>
8431 in the leaves of C<schedule>, where C<contraction> describes how
8432 the domain elements of C<expansion> map to the domain elements
8433 at the original leaves of C<schedule>.
8434 The resulting schedule will contain expansion nodes, unless
8435 C<contraction> is an identity function.
8437 #include <isl/schedule.h>
8438 __isl_give isl_schedule *isl_schedule_expand(
8439 __isl_take isl_schedule *schedule,
8440 __isl_take isl_union_pw_multi_aff *contraction,
8441 __isl_take isl_schedule *expansion);
8443 An C<isl_union_map> representation of the schedule can be obtained
8444 from an C<isl_schedule> using the following function.
8446 #include <isl/schedule.h>
8447 __isl_give isl_union_map *isl_schedule_get_map(
8448 __isl_keep isl_schedule *sched);
8450 The resulting relation encodes the same relative ordering as
8451 the schedule by mapping the domain elements to a common schedule space.
8452 If the schedule_separate_components option is set, then the order
8453 of the children of a set node is explicitly encoded in the result.
8454 If the tree contains any expansion nodes, then the relation
8455 is formulated in terms of the expanded domain elements.
8457 Schedules can be read from input using the following functions.
8459 #include <isl/schedule.h>
8460 __isl_give isl_schedule *isl_schedule_read_from_file(
8461 isl_ctx *ctx, FILE *input);
8462 __isl_give isl_schedule *isl_schedule_read_from_str(
8463 isl_ctx *ctx, const char *str);
8465 A representation of the schedule can be printed using
8467 #include <isl/schedule.h>
8468 __isl_give isl_printer *isl_printer_print_schedule(
8469 __isl_take isl_printer *p,
8470 __isl_keep isl_schedule *schedule);
8471 __isl_give char *isl_schedule_to_str(
8472 __isl_keep isl_schedule *schedule);
8474 C<isl_schedule_to_str> prints the schedule in flow format.
8476 The schedule tree can be traversed through the use of
8477 C<isl_schedule_node> objects that point to a particular
8478 position in the schedule tree. Whenever a C<isl_schedule_node>
8479 is used to modify a node in the schedule tree, the original schedule
8480 tree is left untouched and the modifications are performed to a copy
8481 of the tree. The returned C<isl_schedule_node> then points to
8482 this modified copy of the tree.
8484 The root of the schedule tree can be obtained using the following function.
8486 #include <isl/schedule.h>
8487 __isl_give isl_schedule_node *isl_schedule_get_root(
8488 __isl_keep isl_schedule *schedule);
8490 A pointer to a newly created schedule tree with a single domain
8491 node can be created using the following functions.
8493 #include <isl/schedule_node.h>
8494 __isl_give isl_schedule_node *
8495 isl_schedule_node_from_domain(
8496 __isl_take isl_union_set *domain);
8497 __isl_give isl_schedule_node *
8498 isl_schedule_node_from_extension(
8499 __isl_take isl_union_map *extension);
8501 C<isl_schedule_node_from_extension> creates a tree with an extension
8504 Schedule nodes can be copied and freed using the following functions.
8506 #include <isl/schedule_node.h>
8507 __isl_give isl_schedule_node *isl_schedule_node_copy(
8508 __isl_keep isl_schedule_node *node);
8509 __isl_null isl_schedule_node *isl_schedule_node_free(
8510 __isl_take isl_schedule_node *node);
8512 The following functions can be used to check if two schedule
8513 nodes point to the same position in the same schedule.
8515 #include <isl/schedule_node.h>
8516 isl_bool isl_schedule_node_is_equal(
8517 __isl_keep isl_schedule_node *node1,
8518 __isl_keep isl_schedule_node *node2);
8520 The following properties can be obtained from a schedule node.
8522 #include <isl/schedule_node.h>
8523 enum isl_schedule_node_type isl_schedule_node_get_type(
8524 __isl_keep isl_schedule_node *node);
8525 enum isl_schedule_node_type
8526 isl_schedule_node_get_parent_type(
8527 __isl_keep isl_schedule_node *node);
8528 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8529 __isl_keep isl_schedule_node *node);
8531 The function C<isl_schedule_node_get_type> returns the type of
8532 the node, while C<isl_schedule_node_get_parent_type> returns
8533 type of the parent of the node, which is required to exist.
8534 The function C<isl_schedule_node_get_schedule> returns a copy
8535 to the schedule to which the node belongs.
8537 The following functions can be used to move the schedule node
8538 to a different position in the tree or to check if such a position
8541 #include <isl/schedule_node.h>
8542 isl_bool isl_schedule_node_has_parent(
8543 __isl_keep isl_schedule_node *node);
8544 __isl_give isl_schedule_node *isl_schedule_node_parent(
8545 __isl_take isl_schedule_node *node);
8546 __isl_give isl_schedule_node *isl_schedule_node_root(
8547 __isl_take isl_schedule_node *node);
8548 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8549 __isl_take isl_schedule_node *node,
8551 int isl_schedule_node_n_children(
8552 __isl_keep isl_schedule_node *node);
8553 __isl_give isl_schedule_node *isl_schedule_node_child(
8554 __isl_take isl_schedule_node *node, int pos);
8555 isl_bool isl_schedule_node_has_children(
8556 __isl_keep isl_schedule_node *node);
8557 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8558 __isl_take isl_schedule_node *node);
8559 isl_bool isl_schedule_node_has_previous_sibling(
8560 __isl_keep isl_schedule_node *node);
8561 __isl_give isl_schedule_node *
8562 isl_schedule_node_previous_sibling(
8563 __isl_take isl_schedule_node *node);
8564 isl_bool isl_schedule_node_has_next_sibling(
8565 __isl_keep isl_schedule_node *node);
8566 __isl_give isl_schedule_node *
8567 isl_schedule_node_next_sibling(
8568 __isl_take isl_schedule_node *node);
8570 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8571 is the node itself, the ancestor of generation 1 is its parent and so on.
8573 It is also possible to query the number of ancestors of a node,
8574 the position of the current node
8575 within the children of its parent, the position of the subtree
8576 containing a node within the children of an ancestor
8577 or to obtain a copy of a given
8578 child without destroying the current node.
8579 Given two nodes that point to the same schedule, their closest
8580 shared ancestor can be obtained using
8581 C<isl_schedule_node_get_shared_ancestor>.
8583 #include <isl/schedule_node.h>
8584 int isl_schedule_node_get_tree_depth(
8585 __isl_keep isl_schedule_node *node);
8586 int isl_schedule_node_get_child_position(
8587 __isl_keep isl_schedule_node *node);
8588 int isl_schedule_node_get_ancestor_child_position(
8589 __isl_keep isl_schedule_node *node,
8590 __isl_keep isl_schedule_node *ancestor);
8591 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8592 __isl_keep isl_schedule_node *node, int pos);
8593 __isl_give isl_schedule_node *
8594 isl_schedule_node_get_shared_ancestor(
8595 __isl_keep isl_schedule_node *node1,
8596 __isl_keep isl_schedule_node *node2);
8598 All nodes in a schedule tree or
8599 all descendants of a specific node (including the node) can be visited
8600 in depth-first pre-order using the following functions.
8602 #include <isl/schedule.h>
8603 isl_stat isl_schedule_foreach_schedule_node_top_down(
8604 __isl_keep isl_schedule *sched,
8605 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8606 void *user), void *user);
8608 #include <isl/schedule_node.h>
8609 isl_stat isl_schedule_node_foreach_descendant_top_down(
8610 __isl_keep isl_schedule_node *node,
8611 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8612 void *user), void *user);
8614 The callback function is slightly different from the usual
8615 callbacks in that it not only indicates success (non-negative result)
8616 or failure (negative result), but also indicates whether the children
8617 of the given node should be visited. In particular, if the callback
8618 returns a positive value, then the children are visited, but if
8619 the callback returns zero, then the children are not visited.
8621 The following functions checks whether
8622 all descendants of a specific node (including the node itself)
8623 satisfy a user-specified test.
8625 #include <isl/schedule_node.h>
8626 isl_bool isl_schedule_node_every_descendant(
8627 __isl_keep isl_schedule_node *node,
8628 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8629 void *user), void *user)
8631 The ancestors of a node in a schedule tree can be visited from
8632 the root down to and including the parent of the node using
8633 the following function.
8635 #include <isl/schedule_node.h>
8636 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8637 __isl_keep isl_schedule_node *node,
8638 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8639 void *user), void *user);
8641 The following functions allows for a depth-first post-order
8642 traversal of the nodes in a schedule tree or
8643 of the descendants of a specific node (including the node
8644 itself), where the user callback is allowed to modify the
8647 #include <isl/schedule.h>
8648 __isl_give isl_schedule *
8649 isl_schedule_map_schedule_node_bottom_up(
8650 __isl_take isl_schedule *schedule,
8651 __isl_give isl_schedule_node *(*fn)(
8652 __isl_take isl_schedule_node *node,
8653 void *user), void *user);
8655 #include <isl/schedule_node.h>
8656 __isl_give isl_schedule_node *
8657 isl_schedule_node_map_descendant_bottom_up(
8658 __isl_take isl_schedule_node *node,
8659 __isl_give isl_schedule_node *(*fn)(
8660 __isl_take isl_schedule_node *node,
8661 void *user), void *user);
8663 The traversal continues from the node returned by the callback function.
8664 It is the responsibility of the user to ensure that this does not
8665 lead to an infinite loop. It is safest to always return a pointer
8666 to the same position (same ancestors and child positions) as the input node.
8668 The following function removes a node (along with its descendants)
8669 from a schedule tree and returns a pointer to the leaf at the
8670 same position in the updated tree.
8671 It is not allowed to remove the root of a schedule tree or
8672 a child of a set or sequence node.
8674 #include <isl/schedule_node.h>
8675 __isl_give isl_schedule_node *isl_schedule_node_cut(
8676 __isl_take isl_schedule_node *node);
8678 The following function removes a single node
8679 from a schedule tree and returns a pointer to the child
8680 of the node, now located at the position of the original node
8681 or to a leaf node at that position if there was no child.
8682 It is not allowed to remove the root of a schedule tree,
8683 a set or sequence node, a child of a set or sequence node or
8684 a band node with an anchored subtree.
8686 #include <isl/schedule_node.h>
8687 __isl_give isl_schedule_node *isl_schedule_node_delete(
8688 __isl_take isl_schedule_node *node);
8690 Most nodes in a schedule tree only contain local information.
8691 In some cases, however, a node may also refer to the schedule dimensions
8692 of its outer band nodes.
8693 This means that the position of the node within the tree should
8694 not be changed, or at least that no changes are performed to the
8695 outer band nodes. The following function can be used to test
8696 whether the subtree rooted at a given node contains any such nodes.
8698 #include <isl/schedule_node.h>
8699 isl_bool isl_schedule_node_is_subtree_anchored(
8700 __isl_keep isl_schedule_node *node);
8702 The following function resets the user pointers on all parameter
8703 and tuple identifiers referenced by the given schedule node.
8705 #include <isl/schedule_node.h>
8706 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8707 __isl_take isl_schedule_node *node);
8709 The following function aligns the parameters of the given schedule
8710 node to the given space.
8712 #include <isl/schedule_node.h>
8713 __isl_give isl_schedule_node *
8714 isl_schedule_node_align_params(
8715 __isl_take isl_schedule_node *node,
8716 __isl_take isl_space *space);
8718 Several node types have their own functions for querying
8719 (and in some cases setting) some node type specific properties.
8721 #include <isl/schedule_node.h>
8722 __isl_give isl_space *isl_schedule_node_band_get_space(
8723 __isl_keep isl_schedule_node *node);
8724 __isl_give isl_multi_union_pw_aff *
8725 isl_schedule_node_band_get_partial_schedule(
8726 __isl_keep isl_schedule_node *node);
8727 __isl_give isl_union_map *
8728 isl_schedule_node_band_get_partial_schedule_union_map(
8729 __isl_keep isl_schedule_node *node);
8730 unsigned isl_schedule_node_band_n_member(
8731 __isl_keep isl_schedule_node *node);
8732 isl_bool isl_schedule_node_band_member_get_coincident(
8733 __isl_keep isl_schedule_node *node, int pos);
8734 __isl_give isl_schedule_node *
8735 isl_schedule_node_band_member_set_coincident(
8736 __isl_take isl_schedule_node *node, int pos,
8738 isl_bool isl_schedule_node_band_get_permutable(
8739 __isl_keep isl_schedule_node *node);
8740 __isl_give isl_schedule_node *
8741 isl_schedule_node_band_set_permutable(
8742 __isl_take isl_schedule_node *node, int permutable);
8743 enum isl_ast_loop_type
8744 isl_schedule_node_band_member_get_ast_loop_type(
8745 __isl_keep isl_schedule_node *node, int pos);
8746 __isl_give isl_schedule_node *
8747 isl_schedule_node_band_member_set_ast_loop_type(
8748 __isl_take isl_schedule_node *node, int pos,
8749 enum isl_ast_loop_type type);
8750 __isl_give isl_union_set *
8751 enum isl_ast_loop_type
8752 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8753 __isl_keep isl_schedule_node *node, int pos);
8754 __isl_give isl_schedule_node *
8755 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8756 __isl_take isl_schedule_node *node, int pos,
8757 enum isl_ast_loop_type type);
8758 isl_schedule_node_band_get_ast_build_options(
8759 __isl_keep isl_schedule_node *node);
8760 __isl_give isl_schedule_node *
8761 isl_schedule_node_band_set_ast_build_options(
8762 __isl_take isl_schedule_node *node,
8763 __isl_take isl_union_set *options);
8764 __isl_give isl_set *
8765 isl_schedule_node_band_get_ast_isolate_option(
8766 __isl_keep isl_schedule_node *node);
8768 The function C<isl_schedule_node_band_get_space> returns the space
8769 of the partial schedule of the band.
8770 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8771 returns a representation of the partial schedule of the band node
8772 in the form of an C<isl_union_map>.
8773 The coincident and permutable properties are set by
8774 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8776 A scheduling dimension is considered to be ``coincident''
8777 if it satisfies the coincidence constraints within its band.
8778 That is, if the dependence distances of the coincidence
8779 constraints are all zero in that direction (for fixed
8780 iterations of outer bands).
8781 A band is marked permutable if it was produced using the Pluto-like scheduler.
8782 Note that the scheduler may have to resort to a Feautrier style scheduling
8783 step even if the default scheduler is used.
8784 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8785 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8786 For the meaning of these loop AST generation types and the difference
8787 between the regular loop AST generation type and the isolate
8788 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8789 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8790 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8791 may return C<isl_ast_loop_error> if an error occurs.
8792 The AST build options govern how an AST is generated for
8793 the individual schedule dimensions during AST generation.
8794 See L</"AST Generation Options (Schedule Tree)">.
8795 The isolate option for the given node can be extracted from these
8796 AST build options using the function
8797 C<isl_schedule_node_band_get_ast_isolate_option>.
8799 #include <isl/schedule_node.h>
8800 __isl_give isl_set *
8801 isl_schedule_node_context_get_context(
8802 __isl_keep isl_schedule_node *node);
8804 #include <isl/schedule_node.h>
8805 __isl_give isl_union_set *
8806 isl_schedule_node_domain_get_domain(
8807 __isl_keep isl_schedule_node *node);
8809 #include <isl/schedule_node.h>
8810 __isl_give isl_union_map *
8811 isl_schedule_node_expansion_get_expansion(
8812 __isl_keep isl_schedule_node *node);
8813 __isl_give isl_union_pw_multi_aff *
8814 isl_schedule_node_expansion_get_contraction(
8815 __isl_keep isl_schedule_node *node);
8817 #include <isl/schedule_node.h>
8818 __isl_give isl_union_map *
8819 isl_schedule_node_extension_get_extension(
8820 __isl_keep isl_schedule_node *node);
8822 #include <isl/schedule_node.h>
8823 __isl_give isl_union_set *
8824 isl_schedule_node_filter_get_filter(
8825 __isl_keep isl_schedule_node *node);
8827 #include <isl/schedule_node.h>
8828 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8829 __isl_keep isl_schedule_node *node);
8831 #include <isl/schedule_node.h>
8832 __isl_give isl_id *isl_schedule_node_mark_get_id(
8833 __isl_keep isl_schedule_node *node);
8835 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8836 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8837 partial schedules related to the node.
8839 #include <isl/schedule_node.h>
8840 __isl_give isl_multi_union_pw_aff *
8841 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8842 __isl_keep isl_schedule_node *node);
8843 __isl_give isl_union_pw_multi_aff *
8844 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8845 __isl_keep isl_schedule_node *node);
8846 __isl_give isl_union_map *
8847 isl_schedule_node_get_prefix_schedule_union_map(
8848 __isl_keep isl_schedule_node *node);
8849 __isl_give isl_union_map *
8850 isl_schedule_node_get_prefix_schedule_relation(
8851 __isl_keep isl_schedule_node *node);
8852 __isl_give isl_union_map *
8853 isl_schedule_node_get_subtree_schedule_union_map(
8854 __isl_keep isl_schedule_node *node);
8856 In particular, the functions
8857 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8858 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8859 and C<isl_schedule_node_get_prefix_schedule_union_map>
8860 return a relative ordering on the domain elements that reach the given
8861 node determined by its ancestors.
8862 The function C<isl_schedule_node_get_prefix_schedule_relation>
8863 additionally includes the domain constraints in the result.
8864 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8865 returns a representation of the partial schedule defined by the
8866 subtree rooted at the given node.
8867 If the tree contains any expansion nodes, then the subtree schedule
8868 is formulated in terms of the expanded domain elements.
8869 The tree passed to functions returning a prefix schedule
8870 may only contain extension nodes if these would not affect
8871 the result of these functions. That is, if one of the ancestors
8872 is an extension node, then all of the domain elements that were
8873 added by the extension node need to have been filtered out
8874 by filter nodes between the extension node and the input node.
8875 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8876 may not contain in extension nodes in the selected subtree.
8878 The expansion/contraction defined by an entire subtree, combining
8879 the expansions/contractions
8880 on the expansion nodes in the subtree, can be obtained using
8881 the following functions.
8883 #include <isl/schedule_node.h>
8884 __isl_give isl_union_map *
8885 isl_schedule_node_get_subtree_expansion(
8886 __isl_keep isl_schedule_node *node);
8887 __isl_give isl_union_pw_multi_aff *
8888 isl_schedule_node_get_subtree_contraction(
8889 __isl_keep isl_schedule_node *node);
8891 The total number of outer band members of given node, i.e.,
8892 the shared output dimension of the maps in the result
8893 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8894 using the following function.
8896 #include <isl/schedule_node.h>
8897 int isl_schedule_node_get_schedule_depth(
8898 __isl_keep isl_schedule_node *node);
8900 The following functions return the elements that reach the given node
8901 or the union of universes in the spaces that contain these elements.
8903 #include <isl/schedule_node.h>
8904 __isl_give isl_union_set *
8905 isl_schedule_node_get_domain(
8906 __isl_keep isl_schedule_node *node);
8907 __isl_give isl_union_set *
8908 isl_schedule_node_get_universe_domain(
8909 __isl_keep isl_schedule_node *node);
8911 The input tree of C<isl_schedule_node_get_domain>
8912 may only contain extension nodes if these would not affect
8913 the result of this function. That is, if one of the ancestors
8914 is an extension node, then all of the domain elements that were
8915 added by the extension node need to have been filtered out
8916 by filter nodes between the extension node and the input node.
8918 The following functions can be used to introduce additional nodes
8919 in the schedule tree. The new node is introduced at the point
8920 in the tree where the C<isl_schedule_node> points to and
8921 the results points to the new node.
8923 #include <isl/schedule_node.h>
8924 __isl_give isl_schedule_node *
8925 isl_schedule_node_insert_partial_schedule(
8926 __isl_take isl_schedule_node *node,
8927 __isl_take isl_multi_union_pw_aff *schedule);
8929 This function inserts a new band node with (the greatest integer
8930 part of) the given partial schedule.
8931 The subtree rooted at the given node is assumed not to have
8934 #include <isl/schedule_node.h>
8935 __isl_give isl_schedule_node *
8936 isl_schedule_node_insert_context(
8937 __isl_take isl_schedule_node *node,
8938 __isl_take isl_set *context);
8940 This function inserts a new context node with the given context constraints.
8942 #include <isl/schedule_node.h>
8943 __isl_give isl_schedule_node *
8944 isl_schedule_node_insert_filter(
8945 __isl_take isl_schedule_node *node,
8946 __isl_take isl_union_set *filter);
8948 This function inserts a new filter node with the given filter.
8949 If the original node already pointed to a filter node, then the
8950 two filter nodes are merged into one.
8952 #include <isl/schedule_node.h>
8953 __isl_give isl_schedule_node *
8954 isl_schedule_node_insert_guard(
8955 __isl_take isl_schedule_node *node,
8956 __isl_take isl_set *guard);
8958 This function inserts a new guard node with the given guard constraints.
8960 #include <isl/schedule_node.h>
8961 __isl_give isl_schedule_node *
8962 isl_schedule_node_insert_mark(
8963 __isl_take isl_schedule_node *node,
8964 __isl_take isl_id *mark);
8966 This function inserts a new mark node with the give mark identifier.
8968 #include <isl/schedule_node.h>
8969 __isl_give isl_schedule_node *
8970 isl_schedule_node_insert_sequence(
8971 __isl_take isl_schedule_node *node,
8972 __isl_take isl_union_set_list *filters);
8973 __isl_give isl_schedule_node *
8974 isl_schedule_node_insert_set(
8975 __isl_take isl_schedule_node *node,
8976 __isl_take isl_union_set_list *filters);
8978 These functions insert a new sequence or set node with the given
8979 filters as children.
8981 #include <isl/schedule_node.h>
8982 __isl_give isl_schedule_node *isl_schedule_node_group(
8983 __isl_take isl_schedule_node *node,
8984 __isl_take isl_id *group_id);
8986 This function introduces an expansion node in between the current
8987 node and its parent that expands instances of a space with tuple
8988 identifier C<group_id> to the original domain elements that reach
8989 the node. The group instances are identified by the prefix schedule
8990 of those domain elements. The ancestors of the node are adjusted
8991 to refer to the group instances instead of the original domain
8992 elements. The return value points to the same node in the updated
8993 schedule tree as the input node, i.e., to the child of the newly
8994 introduced expansion node. Grouping instances of different statements
8995 ensures that they will be treated as a single statement by the
8996 AST generator up to the point of the expansion node.
8998 The following function can be used to flatten a nested
9001 #include <isl/schedule_node.h>
9002 __isl_give isl_schedule_node *
9003 isl_schedule_node_sequence_splice_child(
9004 __isl_take isl_schedule_node *node, int pos);
9006 That is, given a sequence node C<node> that has another sequence node
9007 in its child at position C<pos> (in particular, the child of that filter
9008 node is a sequence node), attach the children of that other sequence
9009 node as children of C<node>, replacing the original child at position
9012 The partial schedule of a band node can be scaled (down) or reduced using
9013 the following functions.
9015 #include <isl/schedule_node.h>
9016 __isl_give isl_schedule_node *
9017 isl_schedule_node_band_scale(
9018 __isl_take isl_schedule_node *node,
9019 __isl_take isl_multi_val *mv);
9020 __isl_give isl_schedule_node *
9021 isl_schedule_node_band_scale_down(
9022 __isl_take isl_schedule_node *node,
9023 __isl_take isl_multi_val *mv);
9024 __isl_give isl_schedule_node *
9025 isl_schedule_node_band_mod(
9026 __isl_take isl_schedule_node *node,
9027 __isl_take isl_multi_val *mv);
9029 The spaces of the two arguments need to match.
9030 After scaling, the partial schedule is replaced by its greatest
9031 integer part to ensure that the schedule remains integral.
9033 The partial schedule of a band node can be shifted by an
9034 C<isl_multi_union_pw_aff> with a domain that is a superset
9035 of the domain of the partial schedule using
9036 the following function.
9038 #include <isl/schedule_node.h>
9039 __isl_give isl_schedule_node *
9040 isl_schedule_node_band_shift(
9041 __isl_take isl_schedule_node *node,
9042 __isl_take isl_multi_union_pw_aff *shift);
9044 A band node can be tiled using the following function.
9046 #include <isl/schedule_node.h>
9047 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
9048 __isl_take isl_schedule_node *node,
9049 __isl_take isl_multi_val *sizes);
9051 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
9053 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
9054 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
9056 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
9058 The C<isl_schedule_node_band_tile> function tiles
9059 the band using the given tile sizes inside its schedule.
9060 A new child band node is created to represent the point loops and it is
9061 inserted between the modified band and its children.
9062 The subtree rooted at the given node is assumed not to have
9064 The C<tile_scale_tile_loops> option specifies whether the tile
9065 loops iterators should be scaled by the tile sizes.
9066 If the C<tile_shift_point_loops> option is set, then the point loops
9067 are shifted to start at zero.
9069 A band node can be split into two nested band nodes
9070 using the following function.
9072 #include <isl/schedule_node.h>
9073 __isl_give isl_schedule_node *isl_schedule_node_band_split(
9074 __isl_take isl_schedule_node *node, int pos);
9076 The resulting outer band node contains the first C<pos> dimensions of
9077 the schedule of C<node> while the inner band contains the remaining dimensions.
9078 The schedules of the two band nodes live in anonymous spaces.
9079 The loop AST generation type options and the isolate option
9080 are split over the two band nodes.
9082 A band node can be moved down to the leaves of the subtree rooted
9083 at the band node using the following function.
9085 #include <isl/schedule_node.h>
9086 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
9087 __isl_take isl_schedule_node *node);
9089 The subtree rooted at the given node is assumed not to have
9091 The result points to the node in the resulting tree that is in the same
9092 position as the node pointed to by C<node> in the original tree.
9094 #include <isl/schedule_node.h>
9095 __isl_give isl_schedule_node *
9096 isl_schedule_node_order_before(
9097 __isl_take isl_schedule_node *node,
9098 __isl_take isl_union_set *filter);
9099 __isl_give isl_schedule_node *
9100 isl_schedule_node_order_after(
9101 __isl_take isl_schedule_node *node,
9102 __isl_take isl_union_set *filter);
9104 These functions split the domain elements that reach C<node>
9105 into those that satisfy C<filter> and those that do not and
9106 arranges for the elements that do satisfy the filter to be
9107 executed before (in case of C<isl_schedule_node_order_before>)
9108 or after (in case of C<isl_schedule_node_order_after>)
9109 those that do not. The order is imposed by
9110 a sequence node, possibly reusing the grandparent of C<node>
9111 on two copies of the subtree attached to the original C<node>.
9112 Both copies are simplified with respect to their filter.
9114 Return a pointer to the copy of the subtree that does not
9115 satisfy C<filter>. If there is no such copy (because all
9116 reaching domain elements satisfy the filter), then return
9117 the original pointer.
9119 #include <isl/schedule_node.h>
9120 __isl_give isl_schedule_node *
9121 isl_schedule_node_graft_before(
9122 __isl_take isl_schedule_node *node,
9123 __isl_take isl_schedule_node *graft);
9124 __isl_give isl_schedule_node *
9125 isl_schedule_node_graft_after(
9126 __isl_take isl_schedule_node *node,
9127 __isl_take isl_schedule_node *graft);
9129 This function inserts the C<graft> tree into the tree containing C<node>
9130 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
9131 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
9132 The root node of C<graft>
9133 should be an extension node where the domain of the extension
9134 is the flat product of all outer band nodes of C<node>.
9135 The root node may also be a domain node.
9136 The elements of the domain or the range of the extension may not
9137 intersect with the domain elements that reach "node".
9138 The schedule tree of C<graft> may not be anchored.
9140 The schedule tree of C<node> is modified to include an extension node
9141 corresponding to the root node of C<graft> as a child of the original
9142 parent of C<node>. The original node that C<node> points to and the
9143 child of the root node of C<graft> are attached to this extension node
9144 through a sequence, with appropriate filters and with the child
9145 of C<graft> appearing before or after the original C<node>.
9147 If C<node> already appears inside a sequence that is the child of
9148 an extension node and if the spaces of the new domain elements
9149 do not overlap with those of the original domain elements,
9150 then that extension node is extended with the new extension
9151 rather than introducing a new segment of extension and sequence nodes.
9153 Return a pointer to the same node in the modified tree that
9154 C<node> pointed to in the original tree.
9156 A representation of the schedule node can be printed using
9158 #include <isl/schedule_node.h>
9159 __isl_give isl_printer *isl_printer_print_schedule_node(
9160 __isl_take isl_printer *p,
9161 __isl_keep isl_schedule_node *node);
9162 __isl_give char *isl_schedule_node_to_str(
9163 __isl_keep isl_schedule_node *node);
9165 C<isl_schedule_node_to_str> prints the schedule node in block format.
9167 =head2 Dependence Analysis
9169 C<isl> contains specialized functionality for performing
9170 array dataflow analysis. That is, given a I<sink> access relation,
9171 a collection of possible I<source> accesses and
9172 a collection of I<kill> accesses,
9173 C<isl> can compute relations that describe
9174 for each iteration of the sink access, which iterations
9175 of which of the source access relations may have
9176 accessed the same data element before the given iteration
9177 of the sink access without any intermediate kill of that data element.
9178 The resulting dependence relations map source iterations
9179 to either the corresponding sink iterations or
9180 pairs of corresponding sink iterations and accessed data elements.
9181 To compute standard flow dependences, the sink should be
9182 a read, while the sources should be writes.
9183 If no kills are specified,
9184 then memory based dependence analysis is performed.
9185 If, on the other hand, all sources are also kills,
9186 then value based dependence analysis is performed.
9187 If any of the source accesses are marked as being I<must>
9188 accesses, then they are also treated as kills.
9189 Furthermore, the specification of must-sources results
9190 in the computation of must-dependences.
9191 Only dependences originating in a must access not coscheduled
9192 with any other access to the same element and without
9193 any may accesses between the must access and the sink access
9194 are considered to be must dependences.
9196 =head3 High-level Interface
9198 A high-level interface to dependence analysis is provided
9199 by the following function.
9201 #include <isl/flow.h>
9202 __isl_give isl_union_flow *
9203 isl_union_access_info_compute_flow(
9204 __isl_take isl_union_access_info *access);
9206 The input C<isl_union_access_info> object describes the sink
9207 access relations, the source access relations and a schedule,
9208 while the output C<isl_union_flow> object describes
9209 the resulting dependence relations and the subsets of the
9210 sink relations for which no source was found.
9212 An C<isl_union_access_info> is created, modified, copied and freed using
9213 the following functions.
9215 #include <isl/flow.h>
9216 __isl_give isl_union_access_info *
9217 isl_union_access_info_from_sink(
9218 __isl_take isl_union_map *sink);
9219 __isl_give isl_union_access_info *
9220 isl_union_access_info_set_kill(
9221 __isl_take isl_union_access_info *access,
9222 __isl_take isl_union_map *kill);
9223 __isl_give isl_union_access_info *
9224 isl_union_access_info_set_may_source(
9225 __isl_take isl_union_access_info *access,
9226 __isl_take isl_union_map *may_source);
9227 __isl_give isl_union_access_info *
9228 isl_union_access_info_set_must_source(
9229 __isl_take isl_union_access_info *access,
9230 __isl_take isl_union_map *must_source);
9231 __isl_give isl_union_access_info *
9232 isl_union_access_info_set_schedule(
9233 __isl_take isl_union_access_info *access,
9234 __isl_take isl_schedule *schedule);
9235 __isl_give isl_union_access_info *
9236 isl_union_access_info_set_schedule_map(
9237 __isl_take isl_union_access_info *access,
9238 __isl_take isl_union_map *schedule_map);
9239 __isl_give isl_union_access_info *
9240 isl_union_access_info_copy(
9241 __isl_keep isl_union_access_info *access);
9242 __isl_null isl_union_access_info *
9243 isl_union_access_info_free(
9244 __isl_take isl_union_access_info *access);
9246 The may sources set by C<isl_union_access_info_set_may_source>
9247 do not need to include the must sources set by
9248 C<isl_union_access_info_set_must_source> as a subset.
9249 The kills set by C<isl_union_access_info_set_kill> may overlap
9250 with the may-sources and/or must-sources.
9251 The user is free not to call one (or more) of these functions,
9252 in which case the corresponding set is kept to its empty default.
9253 Similarly, the default schedule initialized by
9254 C<isl_union_access_info_from_sink> is empty.
9255 The current schedule is determined by the last call to either
9256 C<isl_union_access_info_set_schedule> or
9257 C<isl_union_access_info_set_schedule_map>.
9258 The domain of the schedule corresponds to the domains of
9259 the access relations. In particular, the domains of the access
9260 relations are effectively intersected with the domain of the schedule
9261 and only the resulting accesses are considered by the dependence analysis.
9263 An C<isl_union_access_info> object can be read from input
9264 using the following function.
9266 #include <isl/flow.h>
9267 __isl_give isl_union_access_info *
9268 isl_union_access_info_read_from_file(isl_ctx *ctx,
9271 A representation of the information contained in an object
9272 of type C<isl_union_access_info> can be obtained using
9274 #include <isl/flow.h>
9275 __isl_give isl_printer *
9276 isl_printer_print_union_access_info(
9277 __isl_take isl_printer *p,
9278 __isl_keep isl_union_access_info *access);
9279 __isl_give char *isl_union_access_info_to_str(
9280 __isl_keep isl_union_access_info *access);
9282 C<isl_union_access_info_to_str> prints the information in flow format.
9284 The output of C<isl_union_access_info_compute_flow> can be examined,
9285 copied, and freed using the following functions.
9287 #include <isl/flow.h>
9288 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9289 __isl_keep isl_union_flow *flow);
9290 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9291 __isl_keep isl_union_flow *flow);
9292 __isl_give isl_union_map *
9293 isl_union_flow_get_full_must_dependence(
9294 __isl_keep isl_union_flow *flow);
9295 __isl_give isl_union_map *
9296 isl_union_flow_get_full_may_dependence(
9297 __isl_keep isl_union_flow *flow);
9298 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9299 __isl_keep isl_union_flow *flow);
9300 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9301 __isl_keep isl_union_flow *flow);
9302 __isl_give isl_union_flow *isl_union_flow_copy(
9303 __isl_keep isl_union_flow *flow);
9304 __isl_null isl_union_flow *isl_union_flow_free(
9305 __isl_take isl_union_flow *flow);
9307 The relation returned by C<isl_union_flow_get_must_dependence>
9308 relates domain elements of must sources to domain elements of the sink.
9309 The relation returned by C<isl_union_flow_get_may_dependence>
9310 relates domain elements of must or may sources to domain elements of the sink
9311 and includes the previous relation as a subset.
9312 The relation returned by C<isl_union_flow_get_full_must_dependence>
9313 relates domain elements of must sources to pairs of domain elements of the sink
9314 and accessed data elements.
9315 The relation returned by C<isl_union_flow_get_full_may_dependence>
9316 relates domain elements of must or may sources to pairs of
9317 domain elements of the sink and accessed data elements.
9318 This relation includes the previous relation as a subset.
9319 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9320 of the sink relation for which no dependences have been found.
9321 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9322 of the sink relation for which no definite dependences have been found.
9323 That is, it contains those sink access that do not contribute to any
9324 of the elements in the relation returned
9325 by C<isl_union_flow_get_must_dependence>.
9327 A representation of the information contained in an object
9328 of type C<isl_union_flow> can be obtained using
9330 #include <isl/flow.h>
9331 __isl_give isl_printer *isl_printer_print_union_flow(
9332 __isl_take isl_printer *p,
9333 __isl_keep isl_union_flow *flow);
9334 __isl_give char *isl_union_flow_to_str(
9335 __isl_keep isl_union_flow *flow);
9337 C<isl_union_flow_to_str> prints the information in flow format.
9339 =head3 Low-level Interface
9341 A lower-level interface is provided by the following functions.
9343 #include <isl/flow.h>
9345 typedef int (*isl_access_level_before)(void *first, void *second);
9347 __isl_give isl_access_info *isl_access_info_alloc(
9348 __isl_take isl_map *sink,
9349 void *sink_user, isl_access_level_before fn,
9351 __isl_give isl_access_info *isl_access_info_add_source(
9352 __isl_take isl_access_info *acc,
9353 __isl_take isl_map *source, int must,
9355 __isl_null isl_access_info *isl_access_info_free(
9356 __isl_take isl_access_info *acc);
9358 __isl_give isl_flow *isl_access_info_compute_flow(
9359 __isl_take isl_access_info *acc);
9361 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9362 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9363 void *dep_user, void *user),
9365 __isl_give isl_map *isl_flow_get_no_source(
9366 __isl_keep isl_flow *deps, int must);
9367 void isl_flow_free(__isl_take isl_flow *deps);
9369 The function C<isl_access_info_compute_flow> performs the actual
9370 dependence analysis. The other functions are used to construct
9371 the input for this function or to read off the output.
9373 The input is collected in an C<isl_access_info>, which can
9374 be created through a call to C<isl_access_info_alloc>.
9375 The arguments to this functions are the sink access relation
9376 C<sink>, a token C<sink_user> used to identify the sink
9377 access to the user, a callback function for specifying the
9378 relative order of source and sink accesses, and the number
9379 of source access relations that will be added.
9381 The callback function has type C<int (*)(void *first, void *second)>.
9382 The function is called with two user supplied tokens identifying
9383 either a source or the sink and it should return the shared nesting
9384 level and the relative order of the two accesses.
9385 In particular, let I<n> be the number of loops shared by
9386 the two accesses. If C<first> precedes C<second> textually,
9387 then the function should return I<2 * n + 1>; otherwise,
9388 it should return I<2 * n>.
9389 The low-level interface assumes that no sources are coscheduled.
9390 If the information returned by the callback does not allow
9391 the relative order to be determined, then one of the sources
9392 is arbitrarily taken to be executed after the other(s).
9394 The sources can be added to the C<isl_access_info> object by performing
9395 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9396 C<must> indicates whether the source is a I<must> access
9397 or a I<may> access. Note that a multi-valued access relation
9398 should only be marked I<must> if every iteration in the domain
9399 of the relation accesses I<all> elements in its image.
9400 The C<source_user> token is again used to identify
9401 the source access. The range of the source access relation
9402 C<source> should have the same dimension as the range
9403 of the sink access relation.
9404 The C<isl_access_info_free> function should usually not be
9405 called explicitly, because it is already called implicitly by
9406 C<isl_access_info_compute_flow>.
9408 The result of the dependence analysis is collected in an
9409 C<isl_flow>. There may be elements of
9410 the sink access for which no preceding source access could be
9411 found or for which all preceding sources are I<may> accesses.
9412 The relations containing these elements can be obtained through
9413 calls to C<isl_flow_get_no_source>, the first with C<must> set
9414 and the second with C<must> unset.
9415 In the case of standard flow dependence analysis,
9416 with the sink a read and the sources I<must> writes,
9417 the first relation corresponds to the reads from uninitialized
9418 array elements and the second relation is empty.
9419 The actual flow dependences can be extracted using
9420 C<isl_flow_foreach>. This function will call the user-specified
9421 callback function C<fn> for each B<non-empty> dependence between
9422 a source and the sink. The callback function is called
9423 with four arguments, the actual flow dependence relation
9424 mapping source iterations to sink iterations, a boolean that
9425 indicates whether it is a I<must> or I<may> dependence, a token
9426 identifying the source and an additional C<void *> with value
9427 equal to the third argument of the C<isl_flow_foreach> call.
9428 A dependence is marked I<must> if it originates from a I<must>
9429 source and if it is not followed by any I<may> sources.
9431 After finishing with an C<isl_flow>, the user should call
9432 C<isl_flow_free> to free all associated memory.
9434 =head3 Interaction with the Low-level Interface
9436 During the dependence analysis, we frequently need to perform
9437 the following operation. Given a relation between sink iterations
9438 and potential source iterations from a particular source domain,
9439 what is the last potential source iteration corresponding to each
9440 sink iteration. It can sometimes be convenient to adjust
9441 the set of potential source iterations before or after each such operation.
9442 The prototypical example is fuzzy array dataflow analysis,
9443 where we need to analyze if, based on data-dependent constraints,
9444 the sink iteration can ever be executed without one or more of
9445 the corresponding potential source iterations being executed.
9446 If so, we can introduce extra parameters and select an unknown
9447 but fixed source iteration from the potential source iterations.
9448 To be able to perform such manipulations, C<isl> provides the following
9451 #include <isl/flow.h>
9453 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9454 __isl_keep isl_map *source_map,
9455 __isl_keep isl_set *sink, void *source_user,
9457 __isl_give isl_access_info *isl_access_info_set_restrict(
9458 __isl_take isl_access_info *acc,
9459 isl_access_restrict fn, void *user);
9461 The function C<isl_access_info_set_restrict> should be called
9462 before calling C<isl_access_info_compute_flow> and registers a callback function
9463 that will be called any time C<isl> is about to compute the last
9464 potential source. The first argument is the (reverse) proto-dependence,
9465 mapping sink iterations to potential source iterations.
9466 The second argument represents the sink iterations for which
9467 we want to compute the last source iteration.
9468 The third argument is the token corresponding to the source
9469 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9470 The callback is expected to return a restriction on either the input or
9471 the output of the operation computing the last potential source.
9472 If the input needs to be restricted then restrictions are needed
9473 for both the source and the sink iterations. The sink iterations
9474 and the potential source iterations will be intersected with these sets.
9475 If the output needs to be restricted then only a restriction on the source
9476 iterations is required.
9477 If any error occurs, the callback should return C<NULL>.
9478 An C<isl_restriction> object can be created, freed and inspected
9479 using the following functions.
9481 #include <isl/flow.h>
9483 __isl_give isl_restriction *isl_restriction_input(
9484 __isl_take isl_set *source_restr,
9485 __isl_take isl_set *sink_restr);
9486 __isl_give isl_restriction *isl_restriction_output(
9487 __isl_take isl_set *source_restr);
9488 __isl_give isl_restriction *isl_restriction_none(
9489 __isl_take isl_map *source_map);
9490 __isl_give isl_restriction *isl_restriction_empty(
9491 __isl_take isl_map *source_map);
9492 __isl_null isl_restriction *isl_restriction_free(
9493 __isl_take isl_restriction *restr);
9495 C<isl_restriction_none> and C<isl_restriction_empty> are special
9496 cases of C<isl_restriction_input>. C<isl_restriction_none>
9497 is essentially equivalent to
9499 isl_restriction_input(isl_set_universe(
9500 isl_space_range(isl_map_get_space(source_map))),
9502 isl_space_domain(isl_map_get_space(source_map))));
9504 whereas C<isl_restriction_empty> is essentially equivalent to
9506 isl_restriction_input(isl_set_empty(
9507 isl_space_range(isl_map_get_space(source_map))),
9509 isl_space_domain(isl_map_get_space(source_map))));
9513 #include <isl/schedule.h>
9514 __isl_give isl_schedule *
9515 isl_schedule_constraints_compute_schedule(
9516 __isl_take isl_schedule_constraints *sc);
9518 The function C<isl_schedule_constraints_compute_schedule> can be
9519 used to compute a schedule that satisfies the given schedule constraints.
9520 These schedule constraints include the iteration domain for which
9521 a schedule should be computed and dependences between pairs of
9522 iterations. In particular, these dependences include
9523 I<validity> dependences and I<proximity> dependences.
9524 By default, the algorithm used to construct the schedule is similar
9525 to that of C<Pluto>.
9526 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9528 The generated schedule respects all validity dependences.
9529 That is, all dependence distances over these dependences in the
9530 scheduled space are lexicographically positive.
9532 The default algorithm tries to ensure that the dependence distances
9533 over coincidence constraints are zero and to minimize the
9534 dependence distances over proximity dependences.
9535 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9536 for groups of domains where the dependence distances over validity
9537 dependences have only non-negative values.
9538 Note that when minimizing the maximal dependence distance
9539 over proximity dependences, a single affine expression in the parameters
9540 is constructed that bounds all dependence distances. If no such expression
9541 exists, then the algorithm will fail and resort to an alternative
9542 scheduling algorithm. In particular, this means that adding proximity
9543 dependences may eliminate valid solutions. A typical example where this
9544 phenomenon may occur is when some subset of the proximity dependences
9545 has no restriction on some parameter, forcing the coefficient of that
9546 parameter to be zero, while some other subset forces the dependence
9547 distance to depend on that parameter, requiring the same coefficient
9549 When using Feautrier's algorithm, the coincidence and proximity constraints
9550 are only taken into account during the extension to a
9551 full-dimensional schedule.
9553 An C<isl_schedule_constraints> object can be constructed
9554 and manipulated using the following functions.
9556 #include <isl/schedule.h>
9557 __isl_give isl_schedule_constraints *
9558 isl_schedule_constraints_copy(
9559 __isl_keep isl_schedule_constraints *sc);
9560 __isl_give isl_schedule_constraints *
9561 isl_schedule_constraints_on_domain(
9562 __isl_take isl_union_set *domain);
9563 __isl_give isl_schedule_constraints *
9564 isl_schedule_constraints_set_context(
9565 __isl_take isl_schedule_constraints *sc,
9566 __isl_take isl_set *context);
9567 __isl_give isl_schedule_constraints *
9568 isl_schedule_constraints_set_validity(
9569 __isl_take isl_schedule_constraints *sc,
9570 __isl_take isl_union_map *validity);
9571 __isl_give isl_schedule_constraints *
9572 isl_schedule_constraints_set_coincidence(
9573 __isl_take isl_schedule_constraints *sc,
9574 __isl_take isl_union_map *coincidence);
9575 __isl_give isl_schedule_constraints *
9576 isl_schedule_constraints_set_proximity(
9577 __isl_take isl_schedule_constraints *sc,
9578 __isl_take isl_union_map *proximity);
9579 __isl_give isl_schedule_constraints *
9580 isl_schedule_constraints_set_conditional_validity(
9581 __isl_take isl_schedule_constraints *sc,
9582 __isl_take isl_union_map *condition,
9583 __isl_take isl_union_map *validity);
9584 __isl_give isl_schedule_constraints *
9585 isl_schedule_constraints_apply(
9586 __isl_take isl_schedule_constraints *sc,
9587 __isl_take isl_union_map *umap);
9588 __isl_null isl_schedule_constraints *
9589 isl_schedule_constraints_free(
9590 __isl_take isl_schedule_constraints *sc);
9592 The initial C<isl_schedule_constraints> object created by
9593 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9594 That is, it has an empty set of dependences.
9595 The function C<isl_schedule_constraints_set_context> allows the user
9596 to specify additional constraints on the parameters that may
9597 be assumed to hold during the construction of the schedule.
9598 The function C<isl_schedule_constraints_set_validity> replaces the
9599 validity dependences, mapping domain elements I<i> to domain
9600 elements that should be scheduled after I<i>.
9601 The function C<isl_schedule_constraints_set_coincidence> replaces the
9602 coincidence dependences, mapping domain elements I<i> to domain
9603 elements that should be scheduled together with I<I>, if possible.
9604 The function C<isl_schedule_constraints_set_proximity> replaces the
9605 proximity dependences, mapping domain elements I<i> to domain
9606 elements that should be scheduled either before I<I>
9607 or as early as possible after I<i>.
9609 The function C<isl_schedule_constraints_set_conditional_validity>
9610 replaces the conditional validity constraints.
9611 A conditional validity constraint is only imposed when any of the corresponding
9612 conditions is satisfied, i.e., when any of them is non-zero.
9613 That is, the scheduler ensures that within each band if the dependence
9614 distances over the condition constraints are not all zero
9615 then all corresponding conditional validity constraints are respected.
9616 A conditional validity constraint corresponds to a condition
9617 if the two are adjacent, i.e., if the domain of one relation intersect
9618 the range of the other relation.
9619 The typical use case of conditional validity constraints is
9620 to allow order constraints between live ranges to be violated
9621 as long as the live ranges themselves are local to the band.
9622 To allow more fine-grained control over which conditions correspond
9623 to which conditional validity constraints, the domains and ranges
9624 of these relations may include I<tags>. That is, the domains and
9625 ranges of those relation may themselves be wrapped relations
9626 where the iteration domain appears in the domain of those wrapped relations
9627 and the range of the wrapped relations can be arbitrarily chosen
9628 by the user. Conditions and conditional validity constraints are only
9629 considered adjacent to each other if the entire wrapped relation matches.
9630 In particular, a relation with a tag will never be considered adjacent
9631 to a relation without a tag.
9633 The function C<isl_schedule_constraints_apply> takes
9634 schedule constraints that are defined on some set of domain elements
9635 and transforms them to schedule constraints on the elements
9636 to which these domain elements are mapped by the given transformation.
9638 An C<isl_schedule_constraints> object can be inspected
9639 using the following functions.
9641 #include <isl/schedule.h>
9642 __isl_give isl_union_set *
9643 isl_schedule_constraints_get_domain(
9644 __isl_keep isl_schedule_constraints *sc);
9645 __isl_give isl_set *isl_schedule_constraints_get_context(
9646 __isl_keep isl_schedule_constraints *sc);
9647 __isl_give isl_union_map *
9648 isl_schedule_constraints_get_validity(
9649 __isl_keep isl_schedule_constraints *sc);
9650 __isl_give isl_union_map *
9651 isl_schedule_constraints_get_coincidence(
9652 __isl_keep isl_schedule_constraints *sc);
9653 __isl_give isl_union_map *
9654 isl_schedule_constraints_get_proximity(
9655 __isl_keep isl_schedule_constraints *sc);
9656 __isl_give isl_union_map *
9657 isl_schedule_constraints_get_conditional_validity(
9658 __isl_keep isl_schedule_constraints *sc);
9659 __isl_give isl_union_map *
9660 isl_schedule_constraints_get_conditional_validity_condition(
9661 __isl_keep isl_schedule_constraints *sc);
9663 An C<isl_schedule_constraints> object can be read from input
9664 using the following functions.
9666 #include <isl/schedule.h>
9667 __isl_give isl_schedule_constraints *
9668 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9670 __isl_give isl_schedule_constraints *
9671 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9674 The contents of an C<isl_schedule_constraints> object can be printed
9675 using the following functions.
9677 #include <isl/schedule.h>
9678 __isl_give isl_printer *
9679 isl_printer_print_schedule_constraints(
9680 __isl_take isl_printer *p,
9681 __isl_keep isl_schedule_constraints *sc);
9682 __isl_give char *isl_schedule_constraints_to_str(
9683 __isl_keep isl_schedule_constraints *sc);
9685 The following function computes a schedule directly from
9686 an iteration domain and validity and proximity dependences
9687 and is implemented in terms of the functions described above.
9688 The use of C<isl_union_set_compute_schedule> is discouraged.
9690 #include <isl/schedule.h>
9691 __isl_give isl_schedule *isl_union_set_compute_schedule(
9692 __isl_take isl_union_set *domain,
9693 __isl_take isl_union_map *validity,
9694 __isl_take isl_union_map *proximity);
9696 The generated schedule represents a schedule tree.
9697 For more information on schedule trees, see
9698 L</"Schedule Trees">.
9702 #include <isl/schedule.h>
9703 isl_stat isl_options_set_schedule_max_coefficient(
9704 isl_ctx *ctx, int val);
9705 int isl_options_get_schedule_max_coefficient(
9707 isl_stat isl_options_set_schedule_max_constant_term(
9708 isl_ctx *ctx, int val);
9709 int isl_options_get_schedule_max_constant_term(
9711 isl_stat isl_options_set_schedule_serialize_sccs(
9712 isl_ctx *ctx, int val);
9713 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9714 isl_stat isl_options_set_schedule_whole_component(
9715 isl_ctx *ctx, int val);
9716 int isl_options_get_schedule_whole_component(
9718 isl_stat isl_options_set_schedule_maximize_band_depth(
9719 isl_ctx *ctx, int val);
9720 int isl_options_get_schedule_maximize_band_depth(
9722 isl_stat isl_options_set_schedule_maximize_coincidence(
9723 isl_ctx *ctx, int val);
9724 int isl_options_get_schedule_maximize_coincidence(
9726 isl_stat isl_options_set_schedule_outer_coincidence(
9727 isl_ctx *ctx, int val);
9728 int isl_options_get_schedule_outer_coincidence(
9730 isl_stat isl_options_set_schedule_split_scaled(
9731 isl_ctx *ctx, int val);
9732 int isl_options_get_schedule_split_scaled(
9734 isl_stat isl_options_set_schedule_treat_coalescing(
9735 isl_ctx *ctx, int val);
9736 int isl_options_get_schedule_treat_coalescing(
9738 isl_stat isl_options_set_schedule_algorithm(
9739 isl_ctx *ctx, int val);
9740 int isl_options_get_schedule_algorithm(
9742 isl_stat isl_options_set_schedule_carry_self_first(
9743 isl_ctx *ctx, int val);
9744 int isl_options_get_schedule_carry_self_first(
9746 isl_stat isl_options_set_schedule_separate_components(
9747 isl_ctx *ctx, int val);
9748 int isl_options_get_schedule_separate_components(
9753 =item * schedule_max_coefficient
9755 This option enforces that the coefficients for variable and parameter
9756 dimensions in the calculated schedule are not larger than the specified value.
9757 This option can significantly increase the speed of the scheduling calculation
9758 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9759 this option does not introduce bounds on the variable or parameter
9762 =item * schedule_max_constant_term
9764 This option enforces that the constant coefficients in the calculated schedule
9765 are not larger than the maximal constant term. This option can significantly
9766 increase the speed of the scheduling calculation and may also prevent fusing of
9767 unrelated dimensions. A value of -1 means that this option does not introduce
9768 bounds on the constant coefficients.
9770 =item * schedule_serialize_sccs
9772 If this option is set, then all strongly connected components
9773 in the dependence graph are serialized as soon as they are detected.
9774 This means in particular that instances of statements will only
9775 appear in the same band node if these statements belong
9776 to the same strongly connected component at the point where
9777 the band node is constructed.
9779 =item * schedule_whole_component
9781 If this option is set, then entire (weakly) connected
9782 components in the dependence graph are scheduled together
9784 Otherwise, each strongly connected component within
9785 such a weakly connected component is first scheduled separately
9786 and then combined with other strongly connected components.
9787 This option has no effect if C<schedule_serialize_sccs> is set.
9789 =item * schedule_maximize_band_depth
9791 If this option is set, then the scheduler tries to maximize
9792 the width of the bands. Wider bands give more possibilities for tiling.
9793 In particular, if the C<schedule_whole_component> option is set,
9794 then bands are split if this might result in wider bands.
9795 Otherwise, the effect of this option is to only allow
9796 strongly connected components to be combined if this does
9797 not reduce the width of the bands.
9798 Note that if the C<schedule_serialize_sccs> options is set, then
9799 the C<schedule_maximize_band_depth> option therefore has no effect.
9801 =item * schedule_maximize_coincidence
9803 This option is only effective if the C<schedule_whole_component>
9804 option is turned off.
9805 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9806 strongly connected components are only combined with each other
9807 if this does not reduce the number of coincident band members.
9809 =item * schedule_outer_coincidence
9811 If this option is set, then we try to construct schedules
9812 where the outermost scheduling dimension in each band
9813 satisfies the coincidence constraints.
9815 =item * schedule_algorithm
9817 Selects the scheduling algorithm to be used.
9818 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9819 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9821 =item * schedule_split_scaled
9823 If this option is set, then we try to construct schedules in which the
9824 constant term is split off from the linear part if the linear parts of
9825 the scheduling rows for all nodes in the graph have a common non-trivial
9827 The constant term is then dropped and the linear
9829 This option is only effective when the Feautrier style scheduler is
9830 being used, either as the main scheduler or as a fallback for the
9831 Pluto-like scheduler.
9833 =item * schedule_treat_coalescing
9835 If this option is set, then the scheduler will try and avoid
9836 producing schedules that perform loop coalescing.
9837 In particular, for the Pluto-like scheduler, this option places
9838 bounds on the schedule coefficients based on the sizes of the instance sets.
9839 For the Feautrier style scheduler, this option detects potentially
9840 coalescing schedules and then tries to adjust the schedule to avoid
9843 =item * schedule_carry_self_first
9845 If this option is set, then the Feautrier style scheduler
9846 (when used as a fallback for the Pluto-like scheduler) will
9847 first try to only carry self-dependences.
9849 =item * schedule_separate_components
9851 If this option is set then the function C<isl_schedule_get_map>
9852 will treat set nodes in the same way as sequence nodes.
9856 =head2 AST Generation
9858 This section describes the C<isl> functionality for generating
9859 ASTs that visit all the elements
9860 in a domain in an order specified by a schedule tree or
9862 In case the schedule given as a C<isl_union_map>, an AST is generated
9863 that visits all the elements in the domain of the C<isl_union_map>
9864 according to the lexicographic order of the corresponding image
9865 element(s). If the range of the C<isl_union_map> consists of
9866 elements in more than one space, then each of these spaces is handled
9867 separately in an arbitrary order.
9868 It should be noted that the schedule tree or the image elements
9869 in a schedule map only specify the I<order>
9870 in which the corresponding domain elements should be visited.
9871 No direct relation between the partial schedule values
9872 or the image elements on the one hand and the loop iterators
9873 in the generated AST on the other hand should be assumed.
9875 Each AST is generated within a build. The initial build
9876 simply specifies the constraints on the parameters (if any)
9877 and can be created, inspected, copied and freed using the following functions.
9879 #include <isl/ast_build.h>
9880 __isl_give isl_ast_build *isl_ast_build_alloc(
9882 __isl_give isl_ast_build *isl_ast_build_from_context(
9883 __isl_take isl_set *set);
9884 __isl_give isl_ast_build *isl_ast_build_copy(
9885 __isl_keep isl_ast_build *build);
9886 __isl_null isl_ast_build *isl_ast_build_free(
9887 __isl_take isl_ast_build *build);
9889 The C<set> argument is usually a parameter set with zero or more parameters.
9890 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9891 this set is required to be a parameter set.
9892 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9893 specify any parameter constraints.
9894 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9895 and L</"Fine-grained Control over AST Generation">.
9896 Finally, the AST itself can be constructed using one of the following
9899 #include <isl/ast_build.h>
9900 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9901 __isl_keep isl_ast_build *build,
9902 __isl_take isl_schedule *schedule);
9903 __isl_give isl_ast_node *
9904 isl_ast_build_node_from_schedule_map(
9905 __isl_keep isl_ast_build *build,
9906 __isl_take isl_union_map *schedule);
9908 =head3 Inspecting the AST
9910 The basic properties of an AST node can be obtained as follows.
9912 #include <isl/ast.h>
9913 enum isl_ast_node_type isl_ast_node_get_type(
9914 __isl_keep isl_ast_node *node);
9916 The type of an AST node is one of
9917 C<isl_ast_node_for>,
9919 C<isl_ast_node_block>,
9920 C<isl_ast_node_mark> or
9921 C<isl_ast_node_user>.
9922 An C<isl_ast_node_for> represents a for node.
9923 An C<isl_ast_node_if> represents an if node.
9924 An C<isl_ast_node_block> represents a compound node.
9925 An C<isl_ast_node_mark> introduces a mark in the AST.
9926 An C<isl_ast_node_user> represents an expression statement.
9927 An expression statement typically corresponds to a domain element, i.e.,
9928 one of the elements that is visited by the AST.
9930 Each type of node has its own additional properties.
9932 #include <isl/ast.h>
9933 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9934 __isl_keep isl_ast_node *node);
9935 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9936 __isl_keep isl_ast_node *node);
9937 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9938 __isl_keep isl_ast_node *node);
9939 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9940 __isl_keep isl_ast_node *node);
9941 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9942 __isl_keep isl_ast_node *node);
9943 isl_bool isl_ast_node_for_is_degenerate(
9944 __isl_keep isl_ast_node *node);
9946 An C<isl_ast_for> is considered degenerate if it is known to execute
9949 #include <isl/ast.h>
9950 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9951 __isl_keep isl_ast_node *node);
9952 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9953 __isl_keep isl_ast_node *node);
9954 isl_bool isl_ast_node_if_has_else(
9955 __isl_keep isl_ast_node *node);
9956 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9957 __isl_keep isl_ast_node *node);
9959 __isl_give isl_ast_node_list *
9960 isl_ast_node_block_get_children(
9961 __isl_keep isl_ast_node *node);
9963 __isl_give isl_id *isl_ast_node_mark_get_id(
9964 __isl_keep isl_ast_node *node);
9965 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9966 __isl_keep isl_ast_node *node);
9968 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9969 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9971 #include <isl/ast.h>
9972 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9973 __isl_keep isl_ast_node *node);
9975 All descendants of a specific node in the AST (including the node itself)
9977 in depth-first pre-order using the following function.
9979 #include <isl/ast.h>
9980 isl_stat isl_ast_node_foreach_descendant_top_down(
9981 __isl_keep isl_ast_node *node,
9982 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9983 void *user), void *user);
9985 The callback function should return C<isl_bool_true> if the children
9986 of the given node should be visited and C<isl_bool_false> if they should not.
9987 It should return C<isl_bool_error> in case of failure, in which case
9988 the entire traversal is aborted.
9990 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9991 the following functions.
9993 #include <isl/ast.h>
9994 enum isl_ast_expr_type isl_ast_expr_get_type(
9995 __isl_keep isl_ast_expr *expr);
9997 The type of an AST expression is one of
9999 C<isl_ast_expr_id> or
10000 C<isl_ast_expr_int>.
10001 An C<isl_ast_expr_op> represents the result of an operation.
10002 An C<isl_ast_expr_id> represents an identifier.
10003 An C<isl_ast_expr_int> represents an integer value.
10005 Each type of expression has its own additional properties.
10007 #include <isl/ast.h>
10008 enum isl_ast_op_type isl_ast_expr_get_op_type(
10009 __isl_keep isl_ast_expr *expr);
10010 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
10011 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
10012 __isl_keep isl_ast_expr *expr, int pos);
10013 isl_stat isl_ast_expr_foreach_ast_op_type(
10014 __isl_keep isl_ast_expr *expr,
10015 isl_stat (*fn)(enum isl_ast_op_type type,
10016 void *user), void *user);
10017 isl_stat isl_ast_node_foreach_ast_op_type(
10018 __isl_keep isl_ast_node *node,
10019 isl_stat (*fn)(enum isl_ast_op_type type,
10020 void *user), void *user);
10022 C<isl_ast_expr_get_op_type> returns the type of the operation
10023 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
10024 arguments. C<isl_ast_expr_get_op_arg> returns the specified
10026 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
10027 C<isl_ast_op_type> that appears in C<expr>.
10028 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
10029 C<isl_ast_op_type> that appears in C<node>.
10030 The operation type is one of the following.
10034 =item C<isl_ast_op_and>
10036 Logical I<and> of two arguments.
10037 Both arguments can be evaluated.
10039 =item C<isl_ast_op_and_then>
10041 Logical I<and> of two arguments.
10042 The second argument can only be evaluated if the first evaluates to true.
10044 =item C<isl_ast_op_or>
10046 Logical I<or> of two arguments.
10047 Both arguments can be evaluated.
10049 =item C<isl_ast_op_or_else>
10051 Logical I<or> of two arguments.
10052 The second argument can only be evaluated if the first evaluates to false.
10054 =item C<isl_ast_op_max>
10056 Maximum of two or more arguments.
10058 =item C<isl_ast_op_min>
10060 Minimum of two or more arguments.
10062 =item C<isl_ast_op_minus>
10066 =item C<isl_ast_op_add>
10068 Sum of two arguments.
10070 =item C<isl_ast_op_sub>
10072 Difference of two arguments.
10074 =item C<isl_ast_op_mul>
10076 Product of two arguments.
10078 =item C<isl_ast_op_div>
10080 Exact division. That is, the result is known to be an integer.
10082 =item C<isl_ast_op_fdiv_q>
10084 Result of integer division, rounded towards negative
10086 The divisor is known to be positive.
10088 =item C<isl_ast_op_pdiv_q>
10090 Result of integer division, where dividend is known to be non-negative.
10091 The divisor is known to be positive.
10093 =item C<isl_ast_op_pdiv_r>
10095 Remainder of integer division, where dividend is known to be non-negative.
10096 The divisor is known to be positive.
10098 =item C<isl_ast_op_zdiv_r>
10100 Equal to zero iff the remainder on integer division is zero.
10101 The divisor is known to be positive.
10103 =item C<isl_ast_op_cond>
10105 Conditional operator defined on three arguments.
10106 If the first argument evaluates to true, then the result
10107 is equal to the second argument. Otherwise, the result
10108 is equal to the third argument.
10109 The second and third argument may only be evaluated if
10110 the first argument evaluates to true and false, respectively.
10111 Corresponds to C<a ? b : c> in C.
10113 =item C<isl_ast_op_select>
10115 Conditional operator defined on three arguments.
10116 If the first argument evaluates to true, then the result
10117 is equal to the second argument. Otherwise, the result
10118 is equal to the third argument.
10119 The second and third argument may be evaluated independently
10120 of the value of the first argument.
10121 Corresponds to C<a * b + (1 - a) * c> in C.
10123 =item C<isl_ast_op_eq>
10127 =item C<isl_ast_op_le>
10129 Less than or equal relation.
10131 =item C<isl_ast_op_lt>
10133 Less than relation.
10135 =item C<isl_ast_op_ge>
10137 Greater than or equal relation.
10139 =item C<isl_ast_op_gt>
10141 Greater than relation.
10143 =item C<isl_ast_op_call>
10146 The number of arguments of the C<isl_ast_expr> is one more than
10147 the number of arguments in the function call, the first argument
10148 representing the function being called.
10150 =item C<isl_ast_op_access>
10153 The number of arguments of the C<isl_ast_expr> is one more than
10154 the number of index expressions in the array access, the first argument
10155 representing the array being accessed.
10157 =item C<isl_ast_op_member>
10160 This operation has two arguments, a structure and the name of
10161 the member of the structure being accessed.
10165 #include <isl/ast.h>
10166 __isl_give isl_id *isl_ast_expr_get_id(
10167 __isl_keep isl_ast_expr *expr);
10169 Return the identifier represented by the AST expression.
10171 #include <isl/ast.h>
10172 __isl_give isl_val *isl_ast_expr_get_val(
10173 __isl_keep isl_ast_expr *expr);
10175 Return the integer represented by the AST expression.
10177 =head3 Properties of ASTs
10179 #include <isl/ast.h>
10180 isl_bool isl_ast_expr_is_equal(
10181 __isl_keep isl_ast_expr *expr1,
10182 __isl_keep isl_ast_expr *expr2);
10184 Check if two C<isl_ast_expr>s are equal to each other.
10186 =head3 Manipulating and printing the AST
10188 AST nodes can be copied and freed using the following functions.
10190 #include <isl/ast.h>
10191 __isl_give isl_ast_node *isl_ast_node_copy(
10192 __isl_keep isl_ast_node *node);
10193 __isl_null isl_ast_node *isl_ast_node_free(
10194 __isl_take isl_ast_node *node);
10196 AST expressions can be copied and freed using the following functions.
10198 #include <isl/ast.h>
10199 __isl_give isl_ast_expr *isl_ast_expr_copy(
10200 __isl_keep isl_ast_expr *expr);
10201 __isl_null isl_ast_expr *isl_ast_expr_free(
10202 __isl_take isl_ast_expr *expr);
10204 New AST expressions can be created either directly or within
10205 the context of an C<isl_ast_build>.
10207 #include <isl/ast.h>
10208 __isl_give isl_ast_expr *isl_ast_expr_from_val(
10209 __isl_take isl_val *v);
10210 __isl_give isl_ast_expr *isl_ast_expr_from_id(
10211 __isl_take isl_id *id);
10212 __isl_give isl_ast_expr *isl_ast_expr_neg(
10213 __isl_take isl_ast_expr *expr);
10214 __isl_give isl_ast_expr *isl_ast_expr_address_of(
10215 __isl_take isl_ast_expr *expr);
10216 __isl_give isl_ast_expr *isl_ast_expr_add(
10217 __isl_take isl_ast_expr *expr1,
10218 __isl_take isl_ast_expr *expr2);
10219 __isl_give isl_ast_expr *isl_ast_expr_sub(
10220 __isl_take isl_ast_expr *expr1,
10221 __isl_take isl_ast_expr *expr2);
10222 __isl_give isl_ast_expr *isl_ast_expr_mul(
10223 __isl_take isl_ast_expr *expr1,
10224 __isl_take isl_ast_expr *expr2);
10225 __isl_give isl_ast_expr *isl_ast_expr_div(
10226 __isl_take isl_ast_expr *expr1,
10227 __isl_take isl_ast_expr *expr2);
10228 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
10229 __isl_take isl_ast_expr *expr1,
10230 __isl_take isl_ast_expr *expr2);
10231 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
10232 __isl_take isl_ast_expr *expr1,
10233 __isl_take isl_ast_expr *expr2);
10234 __isl_give isl_ast_expr *isl_ast_expr_and(
10235 __isl_take isl_ast_expr *expr1,
10236 __isl_take isl_ast_expr *expr2)
10237 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10238 __isl_take isl_ast_expr *expr1,
10239 __isl_take isl_ast_expr *expr2)
10240 __isl_give isl_ast_expr *isl_ast_expr_or(
10241 __isl_take isl_ast_expr *expr1,
10242 __isl_take isl_ast_expr *expr2)
10243 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10244 __isl_take isl_ast_expr *expr1,
10245 __isl_take isl_ast_expr *expr2)
10246 __isl_give isl_ast_expr *isl_ast_expr_eq(
10247 __isl_take isl_ast_expr *expr1,
10248 __isl_take isl_ast_expr *expr2);
10249 __isl_give isl_ast_expr *isl_ast_expr_le(
10250 __isl_take isl_ast_expr *expr1,
10251 __isl_take isl_ast_expr *expr2);
10252 __isl_give isl_ast_expr *isl_ast_expr_lt(
10253 __isl_take isl_ast_expr *expr1,
10254 __isl_take isl_ast_expr *expr2);
10255 __isl_give isl_ast_expr *isl_ast_expr_ge(
10256 __isl_take isl_ast_expr *expr1,
10257 __isl_take isl_ast_expr *expr2);
10258 __isl_give isl_ast_expr *isl_ast_expr_gt(
10259 __isl_take isl_ast_expr *expr1,
10260 __isl_take isl_ast_expr *expr2);
10261 __isl_give isl_ast_expr *isl_ast_expr_access(
10262 __isl_take isl_ast_expr *array,
10263 __isl_take isl_ast_expr_list *indices);
10264 __isl_give isl_ast_expr *isl_ast_expr_call(
10265 __isl_take isl_ast_expr *function,
10266 __isl_take isl_ast_expr_list *arguments);
10268 The function C<isl_ast_expr_address_of> can be applied to an
10269 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10270 to represent the address of the C<isl_ast_expr_access>.
10271 The second argument of the functions C<isl_ast_expr_pdiv_q> and
10272 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
10274 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10275 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10277 #include <isl/ast_build.h>
10278 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10279 __isl_keep isl_ast_build *build,
10280 __isl_take isl_set *set);
10281 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10282 __isl_keep isl_ast_build *build,
10283 __isl_take isl_pw_aff *pa);
10284 __isl_give isl_ast_expr *
10285 isl_ast_build_access_from_pw_multi_aff(
10286 __isl_keep isl_ast_build *build,
10287 __isl_take isl_pw_multi_aff *pma);
10288 __isl_give isl_ast_expr *
10289 isl_ast_build_access_from_multi_pw_aff(
10290 __isl_keep isl_ast_build *build,
10291 __isl_take isl_multi_pw_aff *mpa);
10292 __isl_give isl_ast_expr *
10293 isl_ast_build_call_from_pw_multi_aff(
10294 __isl_keep isl_ast_build *build,
10295 __isl_take isl_pw_multi_aff *pma);
10296 __isl_give isl_ast_expr *
10297 isl_ast_build_call_from_multi_pw_aff(
10298 __isl_keep isl_ast_build *build,
10299 __isl_take isl_multi_pw_aff *mpa);
10302 the domains of C<pa>, C<mpa> and C<pma> should correspond
10303 to the schedule space of C<build>.
10304 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10305 the function being called.
10306 If the accessed space is a nested relation, then it is taken
10307 to represent an access of the member specified by the range
10308 of this nested relation of the structure specified by the domain
10309 of the nested relation.
10311 The following functions can be used to modify an C<isl_ast_expr>.
10313 #include <isl/ast.h>
10314 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10315 __isl_take isl_ast_expr *expr, int pos,
10316 __isl_take isl_ast_expr *arg);
10318 Replace the argument of C<expr> at position C<pos> by C<arg>.
10320 #include <isl/ast.h>
10321 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10322 __isl_take isl_ast_expr *expr,
10323 __isl_take isl_id_to_ast_expr *id2expr);
10325 The function C<isl_ast_expr_substitute_ids> replaces the
10326 subexpressions of C<expr> of type C<isl_ast_expr_id>
10327 by the corresponding expression in C<id2expr>, if there is any.
10330 User specified data can be attached to an C<isl_ast_node> and obtained
10331 from the same C<isl_ast_node> using the following functions.
10333 #include <isl/ast.h>
10334 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10335 __isl_take isl_ast_node *node,
10336 __isl_take isl_id *annotation);
10337 __isl_give isl_id *isl_ast_node_get_annotation(
10338 __isl_keep isl_ast_node *node);
10340 Basic printing can be performed using the following functions.
10342 #include <isl/ast.h>
10343 __isl_give isl_printer *isl_printer_print_ast_expr(
10344 __isl_take isl_printer *p,
10345 __isl_keep isl_ast_expr *expr);
10346 __isl_give isl_printer *isl_printer_print_ast_node(
10347 __isl_take isl_printer *p,
10348 __isl_keep isl_ast_node *node);
10349 __isl_give char *isl_ast_expr_to_str(
10350 __isl_keep isl_ast_expr *expr);
10351 __isl_give char *isl_ast_node_to_str(
10352 __isl_keep isl_ast_node *node);
10353 __isl_give char *isl_ast_expr_to_C_str(
10354 __isl_keep isl_ast_expr *expr);
10355 __isl_give char *isl_ast_node_to_C_str(
10356 __isl_keep isl_ast_node *node);
10358 The functions C<isl_ast_expr_to_C_str> and
10359 C<isl_ast_node_to_C_str> are convenience functions
10360 that return a string representation of the input in C format.
10362 More advanced printing can be performed using the following functions.
10364 #include <isl/ast.h>
10365 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10366 __isl_take isl_printer *p,
10367 enum isl_ast_op_type type,
10368 __isl_keep const char *name);
10369 isl_stat isl_options_set_ast_print_macro_once(
10370 isl_ctx *ctx, int val);
10371 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10372 __isl_give isl_printer *isl_ast_op_type_print_macro(
10373 enum isl_ast_op_type type,
10374 __isl_take isl_printer *p);
10375 __isl_give isl_printer *isl_ast_expr_print_macros(
10376 __isl_keep isl_ast_expr *expr,
10377 __isl_take isl_printer *p);
10378 __isl_give isl_printer *isl_ast_node_print_macros(
10379 __isl_keep isl_ast_node *node,
10380 __isl_take isl_printer *p);
10381 __isl_give isl_printer *isl_ast_node_print(
10382 __isl_keep isl_ast_node *node,
10383 __isl_take isl_printer *p,
10384 __isl_take isl_ast_print_options *options);
10385 __isl_give isl_printer *isl_ast_node_for_print(
10386 __isl_keep isl_ast_node *node,
10387 __isl_take isl_printer *p,
10388 __isl_take isl_ast_print_options *options);
10389 __isl_give isl_printer *isl_ast_node_if_print(
10390 __isl_keep isl_ast_node *node,
10391 __isl_take isl_printer *p,
10392 __isl_take isl_ast_print_options *options);
10394 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10395 C<isl> may print out an AST that makes use of macros such
10396 as C<floord>, C<min> and C<max>.
10397 The names of these macros may be modified by a call
10398 to C<isl_ast_op_type_set_print_name>. The user-specified
10399 names are associated to the printer object.
10400 C<isl_ast_op_type_print_macro> prints out the macro
10401 corresponding to a specific C<isl_ast_op_type>.
10402 If the print-macro-once option is set, then a given macro definition
10403 is only printed once to any given printer object.
10404 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10405 for subexpressions where these macros would be used and prints
10406 out the required macro definitions.
10407 Essentially, C<isl_ast_expr_print_macros> calls
10408 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10409 as function argument.
10410 C<isl_ast_node_print_macros> does the same
10411 for expressions in its C<isl_ast_node> argument.
10412 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10413 C<isl_ast_node_if_print> print an C<isl_ast_node>
10414 in C<ISL_FORMAT_C>, but allow for some extra control
10415 through an C<isl_ast_print_options> object.
10416 This object can be created using the following functions.
10418 #include <isl/ast.h>
10419 __isl_give isl_ast_print_options *
10420 isl_ast_print_options_alloc(isl_ctx *ctx);
10421 __isl_give isl_ast_print_options *
10422 isl_ast_print_options_copy(
10423 __isl_keep isl_ast_print_options *options);
10424 __isl_null isl_ast_print_options *
10425 isl_ast_print_options_free(
10426 __isl_take isl_ast_print_options *options);
10428 __isl_give isl_ast_print_options *
10429 isl_ast_print_options_set_print_user(
10430 __isl_take isl_ast_print_options *options,
10431 __isl_give isl_printer *(*print_user)(
10432 __isl_take isl_printer *p,
10433 __isl_take isl_ast_print_options *options,
10434 __isl_keep isl_ast_node *node, void *user),
10436 __isl_give isl_ast_print_options *
10437 isl_ast_print_options_set_print_for(
10438 __isl_take isl_ast_print_options *options,
10439 __isl_give isl_printer *(*print_for)(
10440 __isl_take isl_printer *p,
10441 __isl_take isl_ast_print_options *options,
10442 __isl_keep isl_ast_node *node, void *user),
10445 The callback set by C<isl_ast_print_options_set_print_user>
10446 is called whenever a node of type C<isl_ast_node_user> needs to
10448 The callback set by C<isl_ast_print_options_set_print_for>
10449 is called whenever a node of type C<isl_ast_node_for> needs to
10451 Note that C<isl_ast_node_for_print> will I<not> call the
10452 callback set by C<isl_ast_print_options_set_print_for> on the node
10453 on which C<isl_ast_node_for_print> is called, but only on nested
10454 nodes of type C<isl_ast_node_for>. It is therefore safe to
10455 call C<isl_ast_node_for_print> from within the callback set by
10456 C<isl_ast_print_options_set_print_for>.
10458 The following option determines the type to be used for iterators
10459 while printing the AST.
10461 isl_stat isl_options_set_ast_iterator_type(
10462 isl_ctx *ctx, const char *val);
10463 const char *isl_options_get_ast_iterator_type(
10466 The AST printer only prints body nodes as blocks if these
10467 blocks cannot be safely omitted.
10468 For example, a C<for> node with one body node will not be
10469 surrounded with braces in C<ISL_FORMAT_C>.
10470 A block will always be printed by setting the following option.
10472 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10474 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10478 #include <isl/ast_build.h>
10479 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10480 isl_ctx *ctx, int val);
10481 int isl_options_get_ast_build_atomic_upper_bound(
10483 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10485 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10486 isl_stat isl_options_set_ast_build_detect_min_max(
10487 isl_ctx *ctx, int val);
10488 int isl_options_get_ast_build_detect_min_max(
10490 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10491 isl_ctx *ctx, int val);
10492 int isl_options_get_ast_build_exploit_nested_bounds(
10494 isl_stat isl_options_set_ast_build_group_coscheduled(
10495 isl_ctx *ctx, int val);
10496 int isl_options_get_ast_build_group_coscheduled(
10498 isl_stat isl_options_set_ast_build_separation_bounds(
10499 isl_ctx *ctx, int val);
10500 int isl_options_get_ast_build_separation_bounds(
10502 isl_stat isl_options_set_ast_build_scale_strides(
10503 isl_ctx *ctx, int val);
10504 int isl_options_get_ast_build_scale_strides(
10506 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10508 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10509 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10511 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10515 =item * ast_build_atomic_upper_bound
10517 Generate loop upper bounds that consist of the current loop iterator,
10518 an operator and an expression not involving the iterator.
10519 If this option is not set, then the current loop iterator may appear
10520 several times in the upper bound.
10521 For example, when this option is turned off, AST generation
10524 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10528 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10531 When the option is turned on, the following AST is generated
10533 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10536 =item * ast_build_prefer_pdiv
10538 If this option is turned off, then the AST generation will
10539 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10540 operators, but no C<isl_ast_op_pdiv_q> or
10541 C<isl_ast_op_pdiv_r> operators.
10542 If this option is turned on, then C<isl> will try to convert
10543 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10544 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10546 =item * ast_build_detect_min_max
10548 If this option is turned on, then C<isl> will try and detect
10549 min or max-expressions when building AST expressions from
10550 piecewise affine expressions.
10552 =item * ast_build_exploit_nested_bounds
10554 Simplify conditions based on bounds of nested for loops.
10555 In particular, remove conditions that are implied by the fact
10556 that one or more nested loops have at least one iteration,
10557 meaning that the upper bound is at least as large as the lower bound.
10558 For example, when this option is turned off, AST generation
10561 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10567 for (int c0 = 0; c0 <= N; c0 += 1)
10568 for (int c1 = 0; c1 <= M; c1 += 1)
10571 When the option is turned on, the following AST is generated
10573 for (int c0 = 0; c0 <= N; c0 += 1)
10574 for (int c1 = 0; c1 <= M; c1 += 1)
10577 =item * ast_build_group_coscheduled
10579 If two domain elements are assigned the same schedule point, then
10580 they may be executed in any order and they may even appear in different
10581 loops. If this options is set, then the AST generator will make
10582 sure that coscheduled domain elements do not appear in separate parts
10583 of the AST. This is useful in case of nested AST generation
10584 if the outer AST generation is given only part of a schedule
10585 and the inner AST generation should handle the domains that are
10586 coscheduled by this initial part of the schedule together.
10587 For example if an AST is generated for a schedule
10589 { A[i] -> [0]; B[i] -> [0] }
10591 then the C<isl_ast_build_set_create_leaf> callback described
10592 below may get called twice, once for each domain.
10593 Setting this option ensures that the callback is only called once
10594 on both domains together.
10596 =item * ast_build_separation_bounds
10598 This option specifies which bounds to use during separation.
10599 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10600 then all (possibly implicit) bounds on the current dimension will
10601 be used during separation.
10602 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10603 then only those bounds that are explicitly available will
10604 be used during separation.
10606 =item * ast_build_scale_strides
10608 This option specifies whether the AST generator is allowed
10609 to scale down iterators of strided loops.
10611 =item * ast_build_allow_else
10613 This option specifies whether the AST generator is allowed
10614 to construct if statements with else branches.
10616 =item * ast_build_allow_or
10618 This option specifies whether the AST generator is allowed
10619 to construct if conditions with disjunctions.
10623 =head3 AST Generation Options (Schedule Tree)
10625 In case of AST construction from a schedule tree, the options
10626 that control how an AST is created from the individual schedule
10627 dimensions are stored in the band nodes of the tree
10628 (see L</"Schedule Trees">).
10630 In particular, a schedule dimension can be handled in four
10631 different ways, atomic, separate, unroll or the default.
10632 This loop AST generation type can be set using
10633 C<isl_schedule_node_band_member_set_ast_loop_type>.
10635 the first three can be selected by including a one-dimensional
10636 element with as value the position of the schedule dimension
10637 within the band and as name one of C<atomic>, C<separate>
10638 or C<unroll> in the options
10639 set by C<isl_schedule_node_band_set_ast_build_options>.
10640 Only one of these three may be specified for
10641 any given schedule dimension within a band node.
10642 If none of these is specified, then the default
10643 is used. The meaning of the options is as follows.
10649 When this option is specified, the AST generator will make
10650 sure that a given domains space only appears in a single
10651 loop at the specified level.
10653 For example, for the schedule tree
10655 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10657 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10658 options: "{ atomic[x] }"
10660 the following AST will be generated
10662 for (int c0 = 0; c0 <= 10; c0 += 1) {
10669 On the other hand, for the schedule tree
10671 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10673 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10674 options: "{ separate[x] }"
10676 the following AST will be generated
10680 for (int c0 = 1; c0 <= 9; c0 += 1) {
10687 If neither C<atomic> nor C<separate> is specified, then the AST generator
10688 may produce either of these two results or some intermediate form.
10692 When this option is specified, the AST generator will
10693 split the domain of the specified schedule dimension
10694 into pieces with a fixed set of statements for which
10695 instances need to be executed by the iterations in
10696 the schedule domain part. This option tends to avoid
10697 the generation of guards inside the corresponding loops.
10698 See also the C<atomic> option.
10702 When this option is specified, the AST generator will
10703 I<completely> unroll the corresponding schedule dimension.
10704 It is the responsibility of the user to ensure that such
10705 unrolling is possible.
10706 To obtain a partial unrolling, the user should apply an additional
10707 strip-mining to the schedule and fully unroll the inner schedule
10712 The C<isolate> option is a bit more involved. It allows the user
10713 to isolate a range of schedule dimension values from smaller and
10714 greater values. Additionally, the user may specify a different
10715 atomic/separate/unroll choice for the isolated part and the remaining
10716 parts. The typical use case of the C<isolate> option is to isolate
10717 full tiles from partial tiles.
10718 The part that needs to be isolated may depend on outer schedule dimensions.
10719 The option therefore needs to be able to reference those outer schedule
10720 dimensions. In particular, the space of the C<isolate> option is that
10721 of a wrapped map with as domain the flat product of all outer band nodes
10722 and as range the space of the current band node.
10723 The atomic/separate/unroll choice for the isolated part is determined
10724 by an option that lives in an unnamed wrapped space with as domain
10725 a zero-dimensional C<isolate> space and as range the regular
10726 C<atomic>, C<separate> or C<unroll> space.
10727 This option may also be set directly using
10728 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10729 The atomic/separate/unroll choice for the remaining part is determined
10730 by the regular C<atomic>, C<separate> or C<unroll> option.
10731 Since the C<isolate> option references outer schedule dimensions,
10732 its use in a band node causes any tree containing the node
10733 to be considered anchored.
10735 As an example, consider the isolation of full tiles from partial tiles
10736 in a tiling of a triangular domain. The original schedule is as follows.
10738 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10740 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10741 { A[i,j] -> [floor(j/10)] }, \
10742 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10746 for (int c0 = 0; c0 <= 10; c0 += 1)
10747 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10748 for (int c2 = 10 * c0;
10749 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10750 for (int c3 = 10 * c1;
10751 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10754 Isolating the full tiles, we have the following input
10756 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10758 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10759 { A[i,j] -> [floor(j/10)] }, \
10760 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10761 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10762 10a+9+10b+9 <= 100 }"
10767 for (int c0 = 0; c0 <= 8; c0 += 1) {
10768 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10769 for (int c2 = 10 * c0;
10770 c2 <= 10 * c0 + 9; c2 += 1)
10771 for (int c3 = 10 * c1;
10772 c3 <= 10 * c1 + 9; c3 += 1)
10774 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10775 for (int c2 = 10 * c0;
10776 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10777 for (int c3 = 10 * c1;
10778 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10781 for (int c0 = 9; c0 <= 10; c0 += 1)
10782 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10783 for (int c2 = 10 * c0;
10784 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10785 for (int c3 = 10 * c1;
10786 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10790 We may then additionally unroll the innermost loop of the isolated part
10792 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10794 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10795 { A[i,j] -> [floor(j/10)] }, \
10796 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10797 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10798 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10803 for (int c0 = 0; c0 <= 8; c0 += 1) {
10804 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10805 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10807 A(c2, 10 * c1 + 1);
10808 A(c2, 10 * c1 + 2);
10809 A(c2, 10 * c1 + 3);
10810 A(c2, 10 * c1 + 4);
10811 A(c2, 10 * c1 + 5);
10812 A(c2, 10 * c1 + 6);
10813 A(c2, 10 * c1 + 7);
10814 A(c2, 10 * c1 + 8);
10815 A(c2, 10 * c1 + 9);
10817 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10818 for (int c2 = 10 * c0;
10819 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10820 for (int c3 = 10 * c1;
10821 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10824 for (int c0 = 9; c0 <= 10; c0 += 1)
10825 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10826 for (int c2 = 10 * c0;
10827 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10828 for (int c3 = 10 * c1;
10829 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10834 =head3 AST Generation Options (Schedule Map)
10836 In case of AST construction using
10837 C<isl_ast_build_node_from_schedule_map>, the options
10838 that control how an AST is created from the individual schedule
10839 dimensions are stored in the C<isl_ast_build>.
10840 They can be set using the following function.
10842 #include <isl/ast_build.h>
10843 __isl_give isl_ast_build *
10844 isl_ast_build_set_options(
10845 __isl_take isl_ast_build *build,
10846 __isl_take isl_union_map *options);
10848 The options are encoded in an C<isl_union_map>.
10849 The domain of this union relation refers to the schedule domain,
10850 i.e., the range of the schedule passed
10851 to C<isl_ast_build_node_from_schedule_map>.
10852 In the case of nested AST generation (see L</"Nested AST Generation">),
10853 the domain of C<options> should refer to the extra piece of the schedule.
10854 That is, it should be equal to the range of the wrapped relation in the
10855 range of the schedule.
10856 The range of the options can consist of elements in one or more spaces,
10857 the names of which determine the effect of the option.
10858 The values of the range typically also refer to the schedule dimension
10859 to which the option applies, with value C<0> representing
10860 the outermost schedule dimension. In case of nested AST generation
10861 (see L</"Nested AST Generation">), these values refer to the position
10862 of the schedule dimension within the innermost AST generation.
10863 The constraints on the domain elements of
10864 the option should only refer to this dimension and earlier dimensions.
10865 We consider the following spaces.
10869 =item C<separation_class>
10871 B<This option has been deprecated. Use the isolate option on
10872 schedule trees instead.>
10874 This space is a wrapped relation between two one dimensional spaces.
10875 The input space represents the schedule dimension to which the option
10876 applies and the output space represents the separation class.
10877 While constructing a loop corresponding to the specified schedule
10878 dimension(s), the AST generator will try to generate separate loops
10879 for domain elements that are assigned different classes.
10880 If only some of the elements are assigned a class, then those elements
10881 that are not assigned any class will be treated as belonging to a class
10882 that is separate from the explicitly assigned classes.
10883 The typical use case for this option is to separate full tiles from
10885 The other options, described below, are applied after the separation
10888 As an example, consider the separation into full and partial tiles
10889 of a tiling of a triangular domain.
10890 Take, for example, the domain
10892 { A[i,j] : 0 <= i,j and i + j <= 100 }
10894 and a tiling into tiles of 10 by 10. The input to the AST generator
10895 is then the schedule
10897 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10900 Without any options, the following AST is generated
10902 for (int c0 = 0; c0 <= 10; c0 += 1)
10903 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10904 for (int c2 = 10 * c0;
10905 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10907 for (int c3 = 10 * c1;
10908 c3 <= min(10 * c1 + 9, -c2 + 100);
10912 Separation into full and partial tiles can be obtained by assigning
10913 a class, say C<0>, to the full tiles. The full tiles are represented by those
10914 values of the first and second schedule dimensions for which there are
10915 values of the third and fourth dimensions to cover an entire tile.
10916 That is, we need to specify the following option
10918 { [a,b,c,d] -> separation_class[[0]->[0]] :
10919 exists b': 0 <= 10a,10b' and
10920 10a+9+10b'+9 <= 100;
10921 [a,b,c,d] -> separation_class[[1]->[0]] :
10922 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10924 which simplifies to
10926 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10927 a >= 0 and b >= 0 and b <= 8 - a;
10928 [a, b, c, d] -> separation_class[[0] -> [0]] :
10929 a >= 0 and a <= 8 }
10931 With this option, the generated AST is as follows
10934 for (int c0 = 0; c0 <= 8; c0 += 1) {
10935 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10936 for (int c2 = 10 * c0;
10937 c2 <= 10 * c0 + 9; c2 += 1)
10938 for (int c3 = 10 * c1;
10939 c3 <= 10 * c1 + 9; c3 += 1)
10941 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10942 for (int c2 = 10 * c0;
10943 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10945 for (int c3 = 10 * c1;
10946 c3 <= min(-c2 + 100, 10 * c1 + 9);
10950 for (int c0 = 9; c0 <= 10; c0 += 1)
10951 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10952 for (int c2 = 10 * c0;
10953 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10955 for (int c3 = 10 * c1;
10956 c3 <= min(10 * c1 + 9, -c2 + 100);
10963 This is a single-dimensional space representing the schedule dimension(s)
10964 to which ``separation'' should be applied. Separation tries to split
10965 a loop into several pieces if this can avoid the generation of guards
10967 See also the C<atomic> option.
10971 This is a single-dimensional space representing the schedule dimension(s)
10972 for which the domains should be considered ``atomic''. That is, the
10973 AST generator will make sure that any given domain space will only appear
10974 in a single loop at the specified level.
10976 Consider the following schedule
10978 { a[i] -> [i] : 0 <= i < 10;
10979 b[i] -> [i+1] : 0 <= i < 10 }
10981 If the following option is specified
10983 { [i] -> separate[x] }
10985 then the following AST will be generated
10989 for (int c0 = 1; c0 <= 9; c0 += 1) {
10996 If, on the other hand, the following option is specified
10998 { [i] -> atomic[x] }
11000 then the following AST will be generated
11002 for (int c0 = 0; c0 <= 10; c0 += 1) {
11009 If neither C<atomic> nor C<separate> is specified, then the AST generator
11010 may produce either of these two results or some intermediate form.
11014 This is a single-dimensional space representing the schedule dimension(s)
11015 that should be I<completely> unrolled.
11016 To obtain a partial unrolling, the user should apply an additional
11017 strip-mining to the schedule and fully unroll the inner loop.
11021 =head3 Fine-grained Control over AST Generation
11023 Besides specifying the constraints on the parameters,
11024 an C<isl_ast_build> object can be used to control
11025 various aspects of the AST generation process.
11026 In case of AST construction using
11027 C<isl_ast_build_node_from_schedule_map>,
11028 the most prominent way of control is through ``options'',
11029 as explained above.
11031 Additional control is available through the following functions.
11033 #include <isl/ast_build.h>
11034 __isl_give isl_ast_build *
11035 isl_ast_build_set_iterators(
11036 __isl_take isl_ast_build *build,
11037 __isl_take isl_id_list *iterators);
11039 The function C<isl_ast_build_set_iterators> allows the user to
11040 specify a list of iterator C<isl_id>s to be used as iterators.
11041 If the input schedule is injective, then
11042 the number of elements in this list should be as large as the dimension
11043 of the schedule space, but no direct correspondence should be assumed
11044 between dimensions and elements.
11045 If the input schedule is not injective, then an additional number
11046 of C<isl_id>s equal to the largest dimension of the input domains
11048 If the number of provided C<isl_id>s is insufficient, then additional
11049 names are automatically generated.
11051 #include <isl/ast_build.h>
11052 __isl_give isl_ast_build *
11053 isl_ast_build_set_create_leaf(
11054 __isl_take isl_ast_build *build,
11055 __isl_give isl_ast_node *(*fn)(
11056 __isl_take isl_ast_build *build,
11057 void *user), void *user);
11060 C<isl_ast_build_set_create_leaf> function allows for the
11061 specification of a callback that should be called whenever the AST
11062 generator arrives at an element of the schedule domain.
11063 The callback should return an AST node that should be inserted
11064 at the corresponding position of the AST. The default action (when
11065 the callback is not set) is to continue generating parts of the AST to scan
11066 all the domain elements associated to the schedule domain element
11067 and to insert user nodes, ``calling'' the domain element, for each of them.
11068 The C<build> argument contains the current state of the C<isl_ast_build>.
11069 To ease nested AST generation (see L</"Nested AST Generation">),
11070 all control information that is
11071 specific to the current AST generation such as the options and
11072 the callbacks has been removed from this C<isl_ast_build>.
11073 The callback would typically return the result of a nested
11074 AST generation or a
11075 user defined node created using the following function.
11077 #include <isl/ast.h>
11078 __isl_give isl_ast_node *isl_ast_node_alloc_user(
11079 __isl_take isl_ast_expr *expr);
11081 #include <isl/ast_build.h>
11082 __isl_give isl_ast_build *
11083 isl_ast_build_set_at_each_domain(
11084 __isl_take isl_ast_build *build,
11085 __isl_give isl_ast_node *(*fn)(
11086 __isl_take isl_ast_node *node,
11087 __isl_keep isl_ast_build *build,
11088 void *user), void *user);
11089 __isl_give isl_ast_build *
11090 isl_ast_build_set_before_each_for(
11091 __isl_take isl_ast_build *build,
11092 __isl_give isl_id *(*fn)(
11093 __isl_keep isl_ast_build *build,
11094 void *user), void *user);
11095 __isl_give isl_ast_build *
11096 isl_ast_build_set_after_each_for(
11097 __isl_take isl_ast_build *build,
11098 __isl_give isl_ast_node *(*fn)(
11099 __isl_take isl_ast_node *node,
11100 __isl_keep isl_ast_build *build,
11101 void *user), void *user);
11102 __isl_give isl_ast_build *
11103 isl_ast_build_set_before_each_mark(
11104 __isl_take isl_ast_build *build,
11105 isl_stat (*fn)(__isl_keep isl_id *mark,
11106 __isl_keep isl_ast_build *build,
11107 void *user), void *user);
11108 __isl_give isl_ast_build *
11109 isl_ast_build_set_after_each_mark(
11110 __isl_take isl_ast_build *build,
11111 __isl_give isl_ast_node *(*fn)(
11112 __isl_take isl_ast_node *node,
11113 __isl_keep isl_ast_build *build,
11114 void *user), void *user);
11116 The callback set by C<isl_ast_build_set_at_each_domain> will
11117 be called for each domain AST node.
11118 The callbacks set by C<isl_ast_build_set_before_each_for>
11119 and C<isl_ast_build_set_after_each_for> will be called
11120 for each for AST node. The first will be called in depth-first
11121 pre-order, while the second will be called in depth-first post-order.
11122 Since C<isl_ast_build_set_before_each_for> is called before the for
11123 node is actually constructed, it is only passed an C<isl_ast_build>.
11124 The returned C<isl_id> will be added as an annotation (using
11125 C<isl_ast_node_set_annotation>) to the constructed for node.
11126 In particular, if the user has also specified an C<after_each_for>
11127 callback, then the annotation can be retrieved from the node passed to
11128 that callback using C<isl_ast_node_get_annotation>.
11129 The callbacks set by C<isl_ast_build_set_before_each_mark>
11130 and C<isl_ast_build_set_after_each_mark> will be called for each
11131 mark AST node that is created, i.e., for each mark schedule node
11132 in the input schedule tree. The first will be called in depth-first
11133 pre-order, while the second will be called in depth-first post-order.
11134 Since the callback set by C<isl_ast_build_set_before_each_mark>
11135 is called before the mark AST node is actually constructed, it is passed
11136 the identifier of the mark node.
11137 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
11138 The given C<isl_ast_build> can be used to create new
11139 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
11140 or C<isl_ast_build_call_from_pw_multi_aff>.
11142 =head3 Nested AST Generation
11144 C<isl> allows the user to create an AST within the context
11145 of another AST. These nested ASTs are created using the
11146 same C<isl_ast_build_node_from_schedule_map> function that is used to create
11147 the outer AST. The C<build> argument should be an C<isl_ast_build>
11148 passed to a callback set by
11149 C<isl_ast_build_set_create_leaf>.
11150 The space of the range of the C<schedule> argument should refer
11151 to this build. In particular, the space should be a wrapped
11152 relation and the domain of this wrapped relation should be the
11153 same as that of the range of the schedule returned by
11154 C<isl_ast_build_get_schedule> below.
11155 In practice, the new schedule is typically
11156 created by calling C<isl_union_map_range_product> on the old schedule
11157 and some extra piece of the schedule.
11158 The space of the schedule domain is also available from
11159 the C<isl_ast_build>.
11161 #include <isl/ast_build.h>
11162 __isl_give isl_union_map *isl_ast_build_get_schedule(
11163 __isl_keep isl_ast_build *build);
11164 __isl_give isl_space *isl_ast_build_get_schedule_space(
11165 __isl_keep isl_ast_build *build);
11166 __isl_give isl_ast_build *isl_ast_build_restrict(
11167 __isl_take isl_ast_build *build,
11168 __isl_take isl_set *set);
11170 The C<isl_ast_build_get_schedule> function returns a (partial)
11171 schedule for the domains elements for which part of the AST still needs to
11172 be generated in the current build.
11173 In particular, the domain elements are mapped to those iterations of the loops
11174 enclosing the current point of the AST generation inside which
11175 the domain elements are executed.
11176 No direct correspondence between
11177 the input schedule and this schedule should be assumed.
11178 The space obtained from C<isl_ast_build_get_schedule_space> can be used
11179 to create a set for C<isl_ast_build_restrict> to intersect
11180 with the current build. In particular, the set passed to
11181 C<isl_ast_build_restrict> can have additional parameters.
11182 The ids of the set dimensions in the space returned by
11183 C<isl_ast_build_get_schedule_space> correspond to the
11184 iterators of the already generated loops.
11185 The user should not rely on the ids of the output dimensions
11186 of the relations in the union relation returned by
11187 C<isl_ast_build_get_schedule> having any particular value.
11189 =head1 Applications
11191 Although C<isl> is mainly meant to be used as a library,
11192 it also contains some basic applications that use some
11193 of the functionality of C<isl>.
11194 For applications that take one or more polytopes or polyhedra
11195 as input, this input may be specified in either the L<isl format>
11196 or the L<PolyLib format>.
11198 =head2 C<isl_polyhedron_sample>
11200 C<isl_polyhedron_sample> takes a polyhedron as input and prints
11201 an integer element of the polyhedron, if there is any.
11202 The first column in the output is the denominator and is always
11203 equal to 1. If the polyhedron contains no integer points,
11204 then a vector of length zero is printed.
11208 C<isl_pip> takes the same input as the C<example> program
11209 from the C<piplib> distribution, i.e., a set of constraints
11210 on the parameters, a line containing only -1 and finally a set
11211 of constraints on a parametric polyhedron.
11212 The coefficients of the parameters appear in the last columns
11213 (but before the final constant column).
11214 The output is the lexicographic minimum of the parametric polyhedron.
11215 As C<isl> currently does not have its own output format, the output
11216 is just a dump of the internal state.
11218 =head2 C<isl_polyhedron_minimize>
11220 C<isl_polyhedron_minimize> computes the minimum of some linear
11221 or affine objective function over the integer points in a polyhedron.
11222 If an affine objective function
11223 is given, then the constant should appear in the last column.
11225 =head2 C<isl_polytope_scan>
11227 Given a polytope, C<isl_polytope_scan> prints
11228 all integer points in the polytope.
11232 Given an C<isl_union_access_info> object as input,
11233 C<isl_flow> prints out the corresponding dependences,
11234 as computed by C<isl_union_access_info_compute_flow>.
11236 =head2 C<isl_codegen>
11238 Given either a schedule tree or a sequence consisting of
11239 a schedule map, a context set and an options relation,
11240 C<isl_codegen> prints out an AST that scans the domain elements
11241 of the schedule in the order of their image(s) taking into account
11242 the constraints in the context set.
11244 =head2 C<isl_schedule>
11246 Given an C<isl_schedule_constraints> object as input,
11247 C<isl_schedule> prints out a schedule that satisfies the given